







Calculating volume of concrete, dirt, sand, anything. 
20061117 

From Debbie: [This article contains a special calculator to help you find the volume (for example, the cubic yards) of material required to fill (or empty) a space if you know the length, width and depth.]
We are wanting to pour a 24'x30' slab that is 5" deep. How many cubic yards of cement do we need? Answered by Penny Nom. 





1 acre by 3 inches deep 
20181123 

From Cheri: How many yards of soil does it take to cover 1 acre in 3 inches of soil? Answered by Penny Nom. 





Why 1/3 in the volume of a cone? 
20181020 

From Keith: In the formula for the volume of a pyramid, Volume = 1/3 * base * height, where does the 1/3 come from, intuitively? Answered by Penny Nom. 





Filling a candy box 
20181016 

From Stephanie: My child had the question: A candy box has the following measurements.
10x6x4Find the total volume. (We got that one right 240in3)
But... then it said “How many 1/2 inch cubed pieces of candy can fit in the box?
This is where we disagree. Please help. Answered by Penny Nom. 





Covering 6 acres with dirt 
20180927 

From Scott: How many cubic yards of dirt would come from 6 acres, 6 ft. deep? Answered by Penny Nom. 





Covering a region with black Mexican Rock 
20180914 

From Lenton: I have a 48 sq. feet area that I need to cover.
How many cubic ft would I need to cover 48 sq. ft.? Answered by Penny Nom. 





A cube in a cylinder 
20180813 

From Geli: A cylinder with a radius r and height 2r+4 contains a cube with edge length r√2. What fraction of cylinder volume is taken up by the cube Answered by Penny Nom. 





The volume of a berm 
20180604 

From Mike: Have a berm that is 700’ long, 29’ y’all and needs a 20’ top with 51 slope on one side and 31 slope in the other Answered by Penny Nom. 





The volume o a hemisphere 
20180506 

From Sambox: When I have a hemisphere with a volume of 700Pi m^3 what is the radius? Answered by Penny Nom. 





A volume expression for a pyramid 
20180423 

From Shaheer: Do a three sided pyramid and a square pyramid have the same formula if you want to calculate the volume? Answered by Penny Nom. 





Covering a region with mulch 
20180413 

From Roberta: I have a fall zone area of approx. 700 sq ft. that I have to cover with a 6in depth of mulch. How much mulch would I need to purchase? Answered by Penny Nom. 





The volume of a tent with a hexagonal base 
20180327 

From shohel: A tent has its base in the shape of a regular hexagon whose sides are 10m . If the height of the tent is 12m , then find its volume. Answered by Penny Nom. 





The volume of a cube 
20180315 

From Eli: An outdoor art display is a metal cube with edge length 39 feet. What is the volume of the cube in cubic feet? In cubic yards Answered by Penny Nom. 





Water in a cone 
20180210 

From Shuvo: The diagram shows a vertical crosssection of a container in the form
of an inverted cone of height 60 cm and base radius 20 cm. The circular
base is held horizontal and uppermost. Water is pursed into the
container at a constant rate of 40 cm3/s.
Show that, when the depth of water in the container is x cm, the
volume of the water in the container is (πx^3)/27 cm3.
Find the rate of increase of "x" at the instant when "x" = 2. Answered by Penny Nom. 





The volume of a cone without calculus 
20171002 

From Akash: How to find the volume of a cone without the knowledge of calculus? Answered by Penny Nom. 





The volume of an attic 
20170907 

From paul: trying to determine volume of an attic base is rectangular 29 ft by 37 ft
peak runs parallel to longest base side and is 7 ft long
roof lines run from each end of the peak to the respective corners
the peak is 3.5 ft above the base
(so seen from above there are 5 visible lines: the peak and 1 line to each of the 4 corners) Answered by Harley. 





Tons of sand 
20170301 

From Elizabeth: Hello my arena is 132.23 feet width by 132.23 feet length. I need to put 4 inches of sand. How many tons of sand do I need ? Answered by Penny Nom. 





The volume of a hexagonal pyramid 
20161021 

From Elizabeth: Find the height of a hexagonal pyramid with a volume of 1320 ft ^3. The area of the base is 120 ft^2. Answered by Penny Nom. 





The diameter of a cylindrical tin 
20160804 

From Scott: a cylindrical tin is 15 inches high and holds 5 gallons of paint when it is full. Find the diameter of the tin.
(1 gallon = 0.1605 cubic feet) Answered by Penny Nom. 





Cubic feet of soil 
20160619 

From H: A garden is 8 ft x 7 ft that needs to raised 6 inch's How many cubic feet of soil required ? What am I missing ?
Thanks
H Answered by Penny Nom. 





Placing a sphere in a cylinder of water 
20160527 

From Fiona: Hi the question i have is, if I have a cylinder filled with water and the volume of the water is 150Pi what would the rise in the level of the water be if you put a sphere into the cylinder with a volume of 500/3Pi? Sorry if it's a bit long winded Answered by Penny Nom. 





A cylinder in a cube 
20160525 

From Sonia: A cylinder has the same height and diameter as the sides of a cube use 3.14~ which has the greater volume Answered by Penny Nom. 





A trough with a triangular cross section 
20160521 

From Clarice: A trough having an equilateral triangle end sections has sides equal to 0.4 m and 7m long.what is the volume of the liquid in the container if the depth of the water is one half the depth of the trough? Answered by Penny Nom. 





The volume of a truncated rectangular pyramidal pond 
20160513 

From Paul: How do you calculate a partially filled truncated rectangular pyramid if you always know the bottom rectangle, the maximum height top rectangle perimeter, but have a varying height. Similar to filling up a pond you know the current height and dimensions at the max rectangle how do you calculate it half full i.e. 10x30 outside perimeter with a 2x8 base and a max height of 6ft how do you calculate it at 3ft without remeasuring the top perimeter.
Thanks,
Paul Answered by Harley Weston. 





The volume of a cone 
20160331 

From Odum: Find the volume of a cone with radius 6.5cm and height 12.6cm Answered by Penny Nom. 





A tilted cylinder tank 
20160328 

From Astri: I have a problem determining the fluid level for tilted cylinder tank.
Actually I've found some solution here for horizontal cylinder tank. What if the cylinder
is tilted at a certain degree, for example 30 degree from the vertical axis.
Thank you. Answered by Penny Nom. 





The volume of a box with a hexagonal base 
20160327 

From Frank: how many gallons of water in an 8" hexagon shaped box. 6" sides x 12.5" high ? The walls are 1" thick , beveled @ 30 degrees, so inside dimensions are 6" Answered by Penny Nom. 





A square based box and a cylinder 
20160326 

From rajpal: i m trying to calculate an area required to hold 4.4 mln cubic metres of volume.
I used square and I get below result
A box shape that has dimensions 1500 meters (1.5km) by 1500 meters (1.5km) by 2 meters depth has a volume of:
= 4,500,000 cubic meters (4.5 mln cubic meters)
but when I use a cylinder shape, i get below result
A cylindrical shape that has a radius of 850 meters and a depth of 2 meters has a volume of:
= 4,539,600 cubic meters (4.54 mln cubic meters approx)
why is it that the cylinder, though of same depth holds more volume than a square?
kindly clarify. Answered by Penny Nom. 





A rectangular prism 
20160302 

From Paula: Trying to help with a math problem. I don't know how to set up the equation for this.
A rectangular prism has a volume of 7.875m3rd and a height of 3.5 m. What is the area of the base of the prism?
Thanks for your help! Answered by Penny Nom. 





An algebra problem with a sphere 
20160229 

From Sania: If the number of square centimeters on the surface area of a sphere is equal to the number of cubic centimeters in its volume find its diameter Answered by Penny Nom. 





Backfilling a rectangular hole for a shop foundation 
20160208 

From Jeremy: Hello, I'm going to be backfilling a rectangular hole for a shop foundation and need to know how much concrete and gravel I'm going to need to fill it in. The shop foundation is 38 feet wide by 30 feet long and 4 feet deep, there is also a concrete perimeter going inside the foundation that measures 16 inches wide and goes all the way around the inside of the foundation Answered by Penny Nom. 





The volume of a silo 
20160118 

From Clinton: Can you show me how to calculate the ground corn capacity in a steel silos of 10' x 10' high and 10' x 20' high and 10' x 24' high and 10' x 28' high Answered by Penny Nom. 





Water flowing through a rectangular drain 
20160108 

From Tiffany: the cross section of drain is a rectangle 30 cm wide. If water 3.5 cm deep flows through the drain at a rate of 22 cm/s, how many litres of water will flow through in one minute? Answered by Penny Nom. 





Archimedes, Euclid and "Circular Reasoning" 
20151115 

From Ron: I have read about Archimedes and his work with sphere in cylinder and cone in cylinder and the volume relationships. Did he or any others also extend this to regular based polygon based regular like pillars, and columns? The ratio of 1/3 to 1 whole holds true with all regular based columns as example: a regular pyramid having a regular hexagon base inside a regular hexagon column of equal height. Answered by Chris Fisher. 





A volume in cubic yards 
20151112 

From James: The first formula for figuring cubic yards of concrete need is length in feet, times width in feet, times depth in actual inches, divided by 320. Such as, 150x 50 feet x 4inches divided by 320 = cubic yards. How and why does this formula work? Answered by Penny Nom. 





A waste oil tank 
20150613 

From Angela: a waste oil tank is 5 feet wide and 20 feet long, the empty tank on your truck holds 5000 gallons. If 7.48 gallons are in every cubic foot, what is the maximum depth the oil can be to completely fit into your truck? Answered by Penny Nom. 





The volume of a pipe 
20150602 

From gordon: What is the formula to find out how many gallon of water in a length of pipe tried your answer on 8inch at 50feet did not work out Answered by Penny Nom. 





A pile of mulch 
20150515 

From Justin: I have a pile of mulch that measures 19 feet wide at the bottom and has a height of 6 feet. I need to know how many yards of mulch I have.
Please help and help with the formula for further use. Thank you! Answered by Penny Nom. 





The volume of a sphere 
20150430 

From Cassidy: How do you find the radius of a sphere that has volume 36pI? Answered by Penny Nom. 





The volume of a cube 
20150430 

From megan: What's the volume of a cube with a side length of 6? Answered by Penny Nom. 





Constructing a box of maximum volume 
20150414 

From Margot: I need to do a PA for maths and I'm a bit stuck.
The PA is about folding a box with a volume that is as big as possible. The first few questions where really easy but then this one came up.
8. Prove by differentiating that the formula at 7 does indeed give you the maximum volume for each value of z. Answered by Penny Nom. 





Excavating a basement 
20150412 

From Randy: The cost of excavation is $4.50/ cu yd. Find the cost of excavating a basement 87 ft long, 42 ft wide, and 8 ft deep. Answered by Penny Nom. 





A cone of maximum volume 
20150316 

From Mary: I have to use a 8 1/2 inch by 11 inch piece of paper to make a cone that will hold the maximum amount of ice cream possible by only filling it to the top of the cone. I am then supposed to write a function for the volume of my cone and use my graphing calculator to determine the radius and height of the circle. I am so confused, and other than being able to cut the paper into the circle, I do not know where to start. Thank you for your help! Mary Answered by Robert Dawson. 





The volume of a trench 
20150311 

From Kim: A trench 60m long and 15m deep, 12m wide at the top and 8m wide at the bottom.How many cubic meters of earth have been removed? Answered by Penny Nom. 





The volume of a cone 
20150205 

From Linda: How do you calculate the volume of a cone that is 25cm high and has an angle of 20 degrees? Answered by Penny Nom. 





The volume of Lake Utah 
20150129 

From Hannan: Lake Utah has a surface area of 3,846 square miles and an average depth of 10.5 feet. In cubic miles, how much water does it hold?
How would you approach this question? Where would you start? Answered by Robert Dawson and Penny Nom. 





The volume of a swimming pool 
20150121 

From kirara: Find the volume of water in a swimming pool with vertical ends and sides. The length measured at the water line is 50 ft. And the breadth is 20 ft. The bottom of the swimming pool is a plane sloping gradually downward so that the depth of the water at one end is 4 ft. And at the other end is 8 ft. Answered by Penny Nom. 





The volume of a lake 
20150110 

From Peter: If a lake is 8 acres in size and 10 feet deep how many gallons of water does it contain Answered by Penny Nom. 





A silo is composed of a hemisphere and a cylinder 
20150103 

From Ami: A silo is composed of a hemisphere and a cylinder. The total height for the silo is 20m and the diameter of the silo is 8m. What is the volume of the silo to the nearest cubic meter? Answered by Penny Nom. 





A cone is 2/3 full of sand 
20141214 

From Janice: A cone with a radius of 3.5 cm and a height of 12 cm is 2/3 full of sand.
What is the volume of the sand inside? Answered by Penny Nom. 





Doubling the dimensions of a cone 
20141121 

From Hannah: If the volume of a cone of height 10 cm is 261.8 cm3, show that this
volume is increased by a factor of 8 if the dimensions of the cone are doubled. Answered by Penny Nom. 





Using a bucket to fill a tub 
20140827 

From Charlotte: A bathtub needs to be filled with water. To fill the tub, a bucket needs to be filled then dumped into the tub. If the bucket is a cylinder with a radius of 6 in. and a height of 12 in, how many buckets will it take to fill the 5 ft x 3 ft x 3 ft tub. Answered by Penny Nom. 





Bags of sand 
20140606 

From Robert: We have a section that is 20ft long by 14ft wide and 4inches deep, the bags of sand are
.5 cubic ft. How many bags of sand do we need to fill this space evenly. Answered by Penny Nom. 





The volume of a wedge 
20140521 

From steve: I need to figure the volume of a wedge / right triangle, the dimensions of the right triangle is L1(10'5"), L2 (10'6"), H (14'9.5") height of L1 is 0'0" height at intersect L2/H is 3'3" Answered by Penny Nom. 





The volume of hexagonal pyramid and hexagonal prism 
20140518 

From visshwam: how to find volume of hexagonal pyramid and hexagonal prism?
my measurements are each side of pyramid's triangle is 1"x2"x2".
hexagon prism is 2"x1" each side Answered by Penny Nom. 





The volume and radius of a sphere 
20140427 

From grace: How do you find the radius of a sphere when all you know is the volume? Answered by Penny Nom. 





A frustum of a pyramid with a square base 
20140418 

From tuba: a pyramid has a base of 10 m and is 15 m high.what is the volume? if 6m is removed from top what is the volume of the remaining frustum? Answered by Penny Nom. 





A sand trench around a pool 
20140413 

From steve: How sand is needed to back fill a trench around a 24ft dia. pool that is 26" deep by 2ft wide. Making the outside dia. 26ft.
Thank You Answered by Penny Nom. 





A formula for determining concrete volume in cu. yd. 
20140319 

From Steven: I know a couple of formulas for determining concrete volume in cu.yd. the one I use most frequently is length in feet x width in feet x thickness in inch. Divided by 324. It works every time. Where does the number 324 come from. Answered by Penny Nom. 





2 rectangular prisms are similar by a scale of 0.75 
20140316 

From gina: 2 rectangular prisms are similar by a scale of 0.75. The volume of the smaller prism is 27cm3 (cubed). How many cubic centimeters is the volume of the larger prism? Answered by Penny Nom. 





The volume of scale in a pipe 
20140308 

From Sid: What is the estimated volume of scale (Liters) if you have a 12 inch ID pipe,300 feet long with scale 1/2 inch thick. Please show me the method and formula. Thank you for your assistance. Answered by Penny Nom. 





The volume of a cone 
20140208 

From hibba: why is the volume of right circular cone divided by 3? Answered by Penny Nom. 





The volume of a frustum 
20140202 

From mike: volume of frustum R23", r 18", h 16" Answered by Penny Nom. 





A sloped concrete wall 
20131030 

From Brad: We are planning on pouring concrete in a wall form that is sloped. One end is 73 inches tall, and it tapers to 24 inches tall over a distance of 348 inches. It is flat on bottom and sides and is 12 inches thick. Thanks. Answered by Penny Nom. 





Cubic centimeters, milliliters and grams 
20130926 

From Laura: How do I find the volume of a cube with dimensions of .78 cm, .3 cm and .22 cm? Then find the volume in ML and the mass if filled with water? Answered by Penny Nom. 





If the earth was made of a ball of string 
20130918 

From Tammy: My 9 year old son asked me a question and I have no idea how to work it out! Please can you help?
If the earth was made of a ball of string and you unravelled the string how long would it be? Assuming the string is 5mm thick. Answered by Penny Nom. 





The volume of an attic 
20130918 

From David: I have small equipment hut that has a small attic space that I want
to blow insulation into it.
The attic size is shaped like a triangle that is about
8 feet by 10 feet by 7 inches at the highest point.
I need to estimate the volume in square feet or cubic feet to
know how many bags of insulation to blow into the space.
Thanks Answered by Penny Nom. 





Ordering crushed stone 
20130903 

From Prakash: Dear Sirs,
I am working in a Soft Landscaping contracting company. If I need to purchase crushed stone with the size 5070mm for $53,429 m^2$ area, how many 20feet containers should I need to order to my suppliers? The 20foot container has internal dimensions 5,897 mm by 2,348 mm by 2,285 mm and the $53,429 m^2$ area is to be covered by 10 cm of stone. Answered by Harley Weston. 





The volume of a pond 
20130814 

From Kelly: I have a pond that measures 335 feet wide, 385 feet long and 18 feet deep with a 4:1 slope on all four side. How do I figure out how many gallons of water this pond will hold? Answered by Harley Weston. 





A gravel pile in the shape of a triangular pyramid 
20130404 

From Casey: Hello
Right now I am stuck and I feel embarrassed because I feel like the answer is so easy I should know it.
I am working on a project and need to find a volume of gravel it will take to occupy this triangular prism like area. I am not sure what formulas I should use whether it be that for the volume of a pyramid or something more complex? Basically it forms a right triangle at one side then from there all points slope to one singular point about 10412mm away.
I am attaching a picture drawn up in paint with the actual dimensions to clear up any confusion.
Thank you for any help.
Casey Answered by Penny Nom. 





Question 
20130404 

From Casey: Hello
Right now I am stuck and I feel embarrassed because I feel like the answer is so easy I should know it.
I am working on a project and need to find a volume of gravel it will take to occupy this triangular prism like area. I am not sure what formulas I should use whether it be that for the volume of a pyramid or something more complex? Basically it forms a right triangle at one side then from there all points slope to one singular point about 10412mm away.
I am attaching a picture drawn up in paint with the actual dimensions to clear up any confusion.
Thank you for any help.
Casey Answered by Penny Nom. 





A large ditch 
20130111 

From steve: hi
i have a large ditch to make a road entrance accross, the ditch is a green field on one side
and a highway on the other side
the ditch depth is 1.8m on the field side and 3.2 on the highway side
the culvert pipe is 1,2m in diameter
are you with me so far?
the entrance from the highway will be 26m wide tapering in to 6m  ,20 m in from the highway
there will be a concrete slab of 150mm over the top
the fall from highway to field must not exceed 1/8
any ideas how much stone it will need Answered by Harley Weston. 





Filling a box with wood chips 
20121031 

From leeAnne: Each bag of wood chippings will fill 4m3 how bags would be needed?
Volume of box is 572 cm3
L=11CM
W= 6.5CM
H=8CM Answered by Penny Nom. 





A tank with an inner walled compartment 
20121012 

From don: I have a tank 20 feet diameter, 19' 8" tall with an inner walled compartment that has a 7' 6" radius arc with in the tank. I need to figure out the volume of the inner area and the volume of the larger area. Answered by Harley Weston. 





Three piles of top soil 
20121007 

From Steve: I need your help please, I am looking to purchase some top soil and keep getting conflicting answers.
There are 3 piles and here are the sizes;
Pile #1: 203 feet around and 21.29 feet high.
Pile #2: 195 feet around and 18.75 feet high.
Pile #3: 150 feet around and 17.98 feet high.
I look forward to hearing back from you asap.
Thank You!
Steve Answered by Harley Weston. 





The volume of fluid in a tank 
20120906 

From Dave: I have vertical round flat bottom tanks of various dimensions. It is easy to find total volume but I would like to know how to figure out the coversion factor to go from how many centimeters of liquid is in the tank to the number of total cubic meters of volume. So if my float gauge on the tank says there is 50 cm of fluid in the tank, how many cubic meter of total volume is there? Answered by Harley Weston. 





Two cubes 
20120904 

From alexis: a cube has one face that is equal to the total surface area of another cube. Find the ratio of their volumes Answered by Penny Nom. 





The volume of a sphere 
20120818 

From Rohit: why isn't volume of a sphere = Area of a semicircle x the circumference.
i.e. if we revolve a semicircle around its axis we get a sphere Answered by Penny Nom. 





The volume of half an ellipsoid 
20120810 

From Darcy: Hi,
I need to calculate the volume of half an ellipsoid, split horizontally along the long axis. In effect, an oval shaped mound of soil. So the bottom would be an ellipse. I have the length, width and height measurements but not the formula. Thanks! Answered by Robert Dawson and Walter Whiteley. 





A pile of topsoil 
20120723 

From Perry: I have a pile of topsoil that is 42ft long and 16ft tall shaped like a cone how many yards of topsoil do I have. Answered by Penny Nom. 





A volume of revolution 
20120715 

From Tewodros: Let f(x) = e^x and g(x) = x^1/2 both be defined on [0,1]. Consider the region bounded by f(x), g(x), x = 0, x = 1. Rotate this region about the yaxis and determine the volume using the shell method. Answered by Harley Weston. 





A cubical tank 
20120707 

From jake: a storage tank is in the form of a cube. when it is full of water,the volume of water is 15.625 m cube. if the present depth of water is 1.3m, find the volume of water already used from tank Answered by Penny Nom. 





The volume of a wedge 
20120528 

From olwethu: volume of wedge that have side 3,3 cm and 6,2 cm and 20 cm long? Answered by Penny Nom. 





A pyramid on a regular hexagon 
20120414 

From deepak: There is pyramid on a base which is a regular hexagon of side 2a cm.
If every slant edge of this pyramid
is of length 5a/2 cm, than what will be the volume of this pyramid Answered by Penny Nom. 





A lot with a slope 
20120330 

From Carlos: I have a lot with a slope. On the right I need to bring it up 2', From that point to the left is 112' which at this point I need to bring it up 5' for it to be level . The distance front to back is 80'. What is the cubic yards of this area that I need to fill in. Answered by Harley Weston. 





A trapezoidal prism filled with sand 
20120312 

From Maria: could a Trapezoid that is 80 inches high with a 54 inch width top and a 89 inch width bottom and a 80 inch depth hold 58 cubic yards of sand? Answered by Robert Dawson. 





A water tank is in the shape of a truncated cone 
20120308 

From Victoria: Suppose you have a water tank in the shape of a truncated cone. The larger diameter is K, the smaller diameter is K/2, and the height is also K (all measured in meters). The force of gravity on an object of mass, m, is F=9.8m (measured in Newtons). The density of the water is 1000 kilograms per cubic meter. What is the volume of the tank and how much mass will the tank have when it is full? Answered by Penny Nom. 





Measuring the liquid in a horizontal tank 
20120228 

From Philip: I have a steel gas tank that is 3' dia X 5' length. The total volume is 1000 litres.
But how much is left when I use a stick and measure 6" from the bottom or 12" or 24" ??
Is there a formula to use for this task?
Thanks. Answered by Harley Weston. 





The volume of an irregular tetrahedron 
20120222 

From Brittany: If I am given an irregular tetrahedron with the coordinates of the 4 points how do I find the volume? For example I am asked to find the volume and only given the points A(4,3,5), B(2,1,2), C(0,5,0), and D(2,0,0) can you shown me the working and formular to find the volume? Answered by Robert Dawson. 





The volume of a round tube 
20120207 

From I.C: I need to find out how long a 10" round tube needs to be in order for there to be .95 cubic feet of air space Answered by Harley Weston. 





A rectangular block and a sphere 
20120202 

From snehal: a solid rectangular block of metal 49 cm. by 44cm. 18cm. is melted and formed into a solid sphere, find the radius of the sphere[22/7] Answered by Penny Nom. 





The volume of a dugout 
20120128 

From Jan: is there a formula for calculating the cubic yardage removed from a dugout
for example that is forty feet wide by one hundred and twenty feet long by
twelve feet deep with a three to one slope? It is the slope that makes it a
little tricky. Thank you. Answered by Penny Nom. 





How many gallons of water to fill my pool? 
20120113 

From Don: How many gallons of water do you need to fill a 22 feet long and 13 feet wide rectangular pool if it is 3 feet deep on one end and 7 feet deep on the other end? Answered by Penny Nom. 





A volume of revolution 
20120111 

From john: find volume of solid generated by revolving the region in the first quadrant bounded by the curve y squared=x cubed, the line x=4 and the xaxis about the line y=8. The answer in the back of the book is 704 pi divided by5 Answered by Penny Nom. 





The volume of a frustum of a cone 
20111224 

From CV: If I know the height, taper, and volume of a frustum cone,
what are its Radii?
Calculating frustum cone volume is straight forward.
v=Pi/3*h*(R*R+r*r+R*r) where;
v=volume;
h=frustum height;
R=major radius;
r=minor radius;
Pi=3.1415926;
t=taper, ('slant angle' where t=0 is a disk)
Here is the tricky part.
Knowing 'h', 't', & 'v';
Calculate one or both of 'R' & 'r'.
Specifically, what is the formula for 'R=' or 'r='? Answered by Penny Nom. 





The volume of a cylinder 
20111222 

From luke: what is the volume of a cylinder that is 30 mm in diameter and 70 cm high?
can you please write the equation out in full for me to help understand it better. thanks Answered by Penny Nom. 





The volume of a berm 
20111104 

From Roy: I need to know how many cubic yards are in a berm 100 ft long 8 ft high and 32 ft wide at the bottom? Looking from the end of the berm it would look like a trangle. Thanks for the help. Answered by Penny Nom. 





Two great circles 
20111006 

From Jean: "Two great circles lying in planes that are perpendicular to each
other are drawn on a wooden sphere of radius "a". Part of the sphere
is then shaved off in such a way that each cross section of the
remaining solid that is perpendicular to the common diameter of the
two great circles is a square whose vertices lie on these circles.
Find the volume of this solid."
I don't understand the geometry of the problem.
Can you please explain the problem and if possible draw a diagram for me
? Answered by Chris Fisher. 





The volume of a hexagonal prism 
20110919 

From Denise: I am being asked to find the volume of a hexagonal prism, base edges are 3cm, and a height of 15cm. The book that I am working from says that the answer is 77.94cm(cubed) but no matter what the equation I use I always get the answer 116.9/117. Please help! Thank you! Answered by Penny Nom. 





A concrete octagonal pad 
20110804 

From Tina: I have a project where I need to construct a concrete octagonal pad. Each side is 12' and it is 5" deep. Please tell me how to calculate square yards of concrete. Thank you. Answered by Penny Nom. 





The volume of a decagonal prism 
20110529 

From Susan: How do you find the volume of a decagonal prism? Answered by Penny Nom. 





A pipe in a ditch 
20110519 

From Jim: How many cubic feet of stone will it take to fill to six inches around a 4 inch pipe in a ditch 128 ft long x 20 in wide? Answered by Penny Nom. 





The volume of a triangular shaped aquarium 
20110507 

From Jeff: HI, I searched the site but really couldn't find my answer,
at least that I could understand! I have a triangular shaped aquarium
( think of a cube, except its an equal triangle shape). all 3 sides are 48 inches,
and it is 34" tall. Can you please tell me what the volume is in gallons?
Thanks! Answered by Penny Nom. 





A trough of water 
20110501 

From alvin: A trough is formed by nailing together, edge to edge, two boards 11 ft. in length, so that the right section is a right triangle. If a 15 gallon of water are poured into the trough and if the trough is held level so that a right section of water is an isosceles right triangle, how deep is the water? (231cu.in=1 gal.) Answered by Penny Nom. 





The volume of a triangular pyramid 
20110415 

From Chelsea: There is a triangular pyramid which is an equilateral on the base with all sides 16.5 and the height is 25. I have to find the volume. Please help! Answered by Penny Nom. 





The volume of a hopper 
20110413 

From michael: I have a tank that is 72" x 72" at the top and 10" x 10" at the bottom
and is 31" tall. I need to calculate the cubic feet of the tank Answered by Penny Nom. 





The volume of a flower pot 
20110407 

From kp: I have 2 flower pots with the following dimensions that I am trying to calculate the
volume of Soil I will need to fill them. pot #1 29"tall, top of pot 31.5 inches across( radius of 15.5") the bottom of the pot is 21"across (radius 10.5)
Pot #2 29"tall, top of pot 26 across (radius 13") the bottom of the pot 17'"a cross (radius 8.5")
thank you
KP Answered by Penny Nom. 





Volume of concrete 
20110403 

From john: I have 1200 square foot that i need to fill at 4 inches deep. how many cubic yards of concrete will i need? and how do I figure this? Answered by Penny Nom. 





A cubic inch 
20110313 

From wyatt: what is a cubic inch? Answered by Penny Nom. 





How much gravel do I need to make it level? 
20110222 

From Robert: I have an area that is 55 feet long x 75 feet wide and goes from 0 to 13 inches deep. How much gravel do I need to make it level? Answered by Penny Nom. 





Two conical tanks 
20110217 

From rustom: Two vertical conical tanks (both inverted) have their vertices connected by a short horizontal pipe.
One tank, initially full of water, has an altitude of 6 ft. and a diameter of base 7 ft.
The other tank, initially empty, has an altitude of 9 ft., and a diameter of base 8 ft.
If the water is allowed to flow through the connecting pipe, find the level to which
the water will ultimately rise in the empty tank (Neglect the water in the pipe.) Answered by Penny Nom. 





Calibrating a conical tank 
20110205 

From Bill: Hi, I have a round tank with tapered sides where I know the diameter at the top and bottom. Is there a formula I can use to calculate the volume by measuring from the bottom up the side (at the angle of the side) to any given point? Thanks, Bill Answered by Stephen La Rocque and Penny Nom. 





Flipping a cone over 
20110117 

From Fionna: The height of your cone is "x".
Holding the cone so that the vertex is at the bottom, fill it half full with water. The depth of the water is "1/2x".
Put a lid over the top, and flip it over.
What is the new depth of the water, now that the cone is flipped? Answered by Penny Nom. 





The volume of a smokestack 
20110113 

From tom: The outer protective smokestack of a steamship is streamlined so that it has
uniform oval section parallel to the deck. The area of this oval section is
48 sq. ft . If the length of the stack is 15 ft. and the stack is raked aft so
that its axis at its upper end is horizontally 4.2 ft from the lower end, find
the volume enclosed by the stack. Answered by Penny Nom. 





Area and volume of a parallelepiped 
20101214 

From ryan: Got a question, I'm really confused what the question mean and how the diagram would look like... someone please help... Here's the question.
The base of a parallelepiped is a rectangle 4m by 6m. If its lateral edge is 8m and is inclined at an angle 45 degrees to a 6m edge of the base, find the total area and volume of its parallelepiped.
My dilemma is what does it mean by the lateral edge of 8m is inclined at 45 degrees to a 6m edge of the base? Can someone post a diagram to help me solve the promble. Thanks in advance. Answered by Chris Fisher. 





A railway cut 
20101212 

From jade: the pennsylvania railroad found it necessary,owing to land slides upon the roadbed,to reduce the angle of inclination of one bank of certain railway cut near pittsburgh,pa.,from an original angle of 45 degrees to a new angle of 30 degrees. the bank as it originally stood was 200 ft.long and had a slant length of 60 ft.. find the amount of the earth removed, if the top level of the bank remained unchanged. Answered by Penny Nom. 





A water tank has the shape of a right circular cone 
20101207 

From mike: A water tank has the shape of a right circular cone with height 12 feet and radius 8 feet. Water is running into the tank so that the radius r (in feet) of the surface of the water is given by r=0.75t where t is the time (in minutes) that the water has been running. the volume V of the water is given by V=1/3 pi r^2h. Find V(t) and use it to determine the volume of the water when t=5 minutes. Answered by Penny Nom. 





How many gallons of water will it take to fill a classroom? 
20101201 

From deena: How many gallons of water will it take to fill a classroom that is 26 feet long by 19 feet wide and 9 feet high? How many tons of water will that be? Answered by Stephen La Rocque. 





A 400 gallon drum 
20101104 

From Jerry: Question from Jerry:
I want to build A tank. able to hold 400 gallons of asphalt sealer it will be round . basically like A old fuel oil drum but made with heavy material . math ? was I want tank to hold 400 gallons I think the length of 60" would be perfect. I don't know what diameter or radius of tank needs to be . to make it A 400 Gallon tank Answered by Harley Weston. 





The weight of some dirt 
20101103 

From Maggie: I am wanting to know how many tons of dirt we r going to need to fill a basement.
The measurements we r going with r 15ftx15ftx8ft. Answered by Penny Nom. 





A water trough 
20101022 

From Jasmine: A water trough is 8 m long and its crosssection is an isosceles
trapezoid which is 90 cm wide at the bottom and 120 cm wide
at the top, and the height is 30 cm. The trough is not full.
Give an expression for V , the volume of water in the trough in cm^3,
when the depth of the water is d cm. Answered by Stephen La Rocque. 





Cleaning a ditch 
20101020 

From bill: how many yards of dirt will be removed from a ditch 200 feet long
6 feet wide at top x 3 feet wide at bottom and 4 foot slopes Answered by Penny Nom. 





The volume of a truncated pyramid 
20101012 

From A: what is the formula to find out volume of a pyramid with individual length and breadth? For example bottom size is 6.5m x 6.5m, top size 1.5m x 4.2m and height 0.8m. please send me the formula. Answered by Stephen La Rocque. 





30,000 US gallons of water 
20101012 

From mike: If a swimming pool can hold 30,000 US gallons of water  is it possible to calculate the number of yards of dirt it would take to fill the hole? Answered by Penny Nom. 





Cost of a driveway 
20101011 

From arlene: What is the total cost of a driveway that is 25' wide and 45' long with 4" thickness if the concreat cost 92.00 per cubic yard and labor is 70.00 a cubic yard? Answered by Stephen La Rocque. 





Mr Thorpe's volume 
20100815 

From thomas: A circular pool has a diameter of 3m and is filled to a depth of 70 cm. Mr Thorpe climbs into the pool and submerges for ten seconds while his son measures the new depth at 72 cm. Calculate Mr Thorpe’s volume. Answered by Penny Nom. 





Digging a pond 
20100814 

From Jody: I am digging a pond that is 100' X 60' X 10' deep in the centre. All four sides will have 31 slopes on them. How do I calculate how may yards of material will have to be removed? Answered by Tyler Wood. 





80,000 yards of dirt 
20100812 

From Jeremy: If I have an area 50' x 1200', what would be the elevation with 80,000 yards of dirt on it. Answered by Robert Dawson. 





The volume of earth to be moved 
20100729 

From Michael: Volume of earth moved @ 500' across, 1 to 3 degree slope, 30' deep X 50' across at the bottom. Answered by Stephen La Rocque and Harley Weston. 





Thickness of sand 
20100707 

From RHONDA: In an 18 x 33 ft area how much is 4 yards of sand in inches to cover this area. Answered by Penny Nom. 





How many gallons do I need to finish filling the tank? 
20100614 

From Bruce: I have a tank on it's side. 44" dia. by 72" long, I'm 6" from having tank full. How many gallons do I need to finish filling tank? Answered by Harley Weston. 





A fuel tank with a broken gage 
20100528 

From Kinsley: Hello, I have a fuel tank with a broken gage. It is a 2000 gallon tank. The dimensions are 64" dia. x 146" long. The fuel gage doesn't work, so the only measurement I can do is put a stick in it to see what is left. Currently it is at 19". PLEASE NOTE: the tank is laying on its side, meaning the long side is on the ground. So, how do I determine how much fuel is in the tank by the inches remaining? Thank you very much. Answered by Tyler Wood. 





Liquid in a horizontal tank 
20100526 

From Brian: I have a 50' long tank by 12' diameter it is lying down on it side with 12" of Liquid in the bottom i need to know how many gallons of fluid this is? Please Help, I was able to calculate out the Triangle but not the Sector! Answered by Harley Weston. 





How many bags will it take to fill this? 
20100522 

From David: A garden lot..360 square feet and 6 inches deep..you want to fill this with mulch and use 2 cubic. foot bags...how many bags will it take to fill this? Thank you...Dave Answered by Tyler Wood. 





The volume of a test tube 
20100520 

From Nick: A maths question. I have a test tube (basically a cylinder but with a rounded
bottom end) and the measurements are: the diameter or width of the tube is
31mm and the total length of the whole tube is 204mm. The question is:
(a) what's the volume of this test tube (rounded to the nearest cubic mm) and
(b) what's the capacity of this test tube (rounded to the nearest mL).
I need to show the full mathematical workings out of the two, not just the
answer. The problem is the circular bottom end of the tube, it isn't flat, that
would make it rather "easy"or straightforward but this is a halfcircle
(like all test tubes are)!! Answered by Penny Nom. 





A conical pile of gravel 
20100515 

From Chuck: If I have a conical pile of gravel 50 feet across at the base and a height of 65 feet and
the slope of the side is approximately 60 degrees, how do I calculate the cubic yards? Answered by Robert Dawson. 





88 litres of oil in a cylinder 
20100515 

From fella: 88 litres of oil are poured into a drum 40 cm in diameter. find the depth of the oil in the drum. Answered by Penny Nom. 





A conical pile of gravel 
20100413 

From Chassity: The gravel pile is 120' around at the base and goes up 20' high at the peak. How many tons or yards of gravel in that pile? Answered by Penny Nom. 





Volume of a cylinder 
20100412 

From Louis: A hockey puck has a diameter of 7.5 cm and a thickness of 2.5 cm.
What is its Volume?
A copper pipe with an inside diameter of 1cm. is 4m long.
What volume of water (in cm3) can it hold? Answered by Tyler Wood. 





A cube with twice the volume 
20100411 

From Woojin: From a given cube create another cube with twice the volume.
the cube: 5cm each. Answered by Tyler Wood. 





Backfilling the area around the outside of a pool 
20100407 

From Craig: I need to get dirt to fill an area 25ft x 25ft (think of a giant sandbox) HOWEVER, there is a pool 18 ft round in the middle of it. We need to backfill the area around the outside of the pool 6" deep. How much dirt will I need? Answered by Penny Nom. 





The volume of a berm 
20100405 

From jim: a berm 6 ft wide x 112 ft long 18 inches high at center x 18 inches down to 0 front and back as a taper...how much soil do I need? Answered by Penny Nom. 





Pyramids and parallelograms 
20100401 

From Vivi: Hi, my name is Vivi, and math teacher is giving a geometry test. I tend to forget how to find the surface area and volume of triangular pyramids and parallelograms. Do you have a way of remembering how to find the surface area? Answered by Harley Weston. 





A rectangular box packed with cylinders 
20100316 

From Laura: There is a cylinder which has a diameter of 10cm and height of 10 cm. Work out the volume of the cylinder. Then in a packed box of 20 cylinders (height of box 10cm) work out the volume inside the box that is not filled by the cylinders give your answer in terms of pi. Answered by Penny Nom. 





The volume of a frusta of a hexagonal based pyramid 
20100304 

From sarah: Volume of a frusta of a hexagonal based pyramid Answered by Penny Nom. 





A paper tube 
20100221 

From shailesh: How can i estimate weight of paper tube from size. i have paper tube
inner diameter : 22mm, thickness : 2mm, length : 14mm. so how can i got weight
of paper tube? Answered by Harley Weston and Tyler Wood. 





A prism and a pyramid 
20100219 

From Juanita: What is the relationship between the volume of a prism and a pyramid with congruent base areas and heights? Answered by Tyler Wood. 





A dirt berm 
20100205 

From casey: My question is two fold. I want to build a dirt berm that is 95 feet long and 8 feet high which has a 45 degree angle on each side of the slope. My first question is how wide will the berm end up being? Second question is how many cubic yards of dirt will I need to get? Thanks! Answered by Harley Weston. 





Aggregate must for a road base 
20100130 

From Bryan: How many cubic yards of aggregate must be ordered for a road base 16 in. thick and 2 miles long with a top width of 30 ft, if the side slopes are one on one, or 45 degrees Answered by Stephen La Rocque. 





The volume of a silo 
20100121 

From heather: The height of the silo is 30ft and the face that rests against a barn is 10 ft wide. If the barn if 5 ft from the center of the silo what is the capacity of the silo? Answered by Penny Nom. 





The length of a sidewalk 
20100119 

From Les: I have a sidewalk 4"thick,4ft. wide,and I have 2cubic yards of concrete. What is the length of my sidewalk? Answered by Penny Nom. 





The volume of an ellipsoid 
20100101 

From Barbara: I need to calculate the volume of an ellipsoid with the dimensions:
102.5 mm x 57 mm x 57 mm = L x W x H
I am using the formula V = 4/3 pi (.5L)(.5W)(.5H), but it isn't giving me a reasonable
number. Answered by Penny Nom. 





The volume of a frustum 
20091229 

From dave: I have a frustum top 1.7r bottom .55r and 2.14 h
I have to calculate cement in a silo every week.
I am not very good at maths but i have been adding the top and bottom
to get an average so as to turn it into a cylinder and i come up with
8.5m3 I know that the correct volume is 9.24 m3. Can you tell me why
getting an average width on the top and bottom of a frustum doesn't work.
Thank you. Answered by Chris Fisher. 





Truncated Octagonal Prism 
20091226 

From freitas: the top plane of the truncated octagonal right prism is 45 degree with respect to horizontal. find the volume Answered by Janice Cotcher. 





The volume of a compost pile 
20091211 

From Tim: I have a pile of compost that is78 feet long by 18 feet wide at base by 9
feet tall to a point. At the width it looks like a triangle
I'm looking for the square yards
Thanks Answered by Penny Nom. 





Dirt around a cylinder 
20091210 

From curtis: If I was to pile 3.5 cu. yds of dirt around a 5ft 6in. diameter cylinder within 24in. of the outside, how high will the dirt be? Answered by Penny Nom. 





A 24" circumference pipe 
20091121 

From Cliff: How long does a pipe with a 24" circumference need to be to hold 2 cubic feet? Answered by Penny Nom. 





A triangular shaped ditch 
20091112 

From Tim: I am planning on constructing a triangular shaped ditch the measures 550 meters in length, 6 meters wide at the surface, .3048 meters at the invert of the ditch and 2 meters deep.
How many cubic meters of material will have to be excavated to construct
this ditch Answered by Robert Dawson. 





Fill required for a driveway 
20091003 

From Rose: We are going to be pouring a driveway and it is needing a lot of fill. I can't seem to figure this out. Measurements are 30 ft x 30 ft and it goes from 2' deep to 4" (which is what I need overall as it will be 4" of concrete for the driveway. Please HELP Rose in GA. Answered by Penny Nom. 





The volume of a levee 
20090929 

From Wes: I need a levee with a 2:1 slope on both sides (front and back), the length
of the levee is 290 feet, the height of the levee is 15 feet, and the width
of the levee, at the top, is 10 feet. How do I figure out how many CUBIC
YARDS of dirt I need to make the levee? And what formula do I use in
future to figure this out easily? Answered by Penny Nom. 





The volume of a garbage bag 
20090928 

From Steve: I have often wondered how a garbage bags is determined in gallons 
many different manufactures of these type bags often have different sizes
stating they are a (for example) a 55 gallon bag 
also I see some that show a range (2030 gallon)
yet is a specific size (16 x 14 x39 or a 30 x 36)
I have searched and search but have been unable to find a formula Answered by Robert Dawson. 





Cubic feet of concrete 
20090924 

From aLAN: How many CF of concrete does it take to pour a 1000 SF area with concrete at 4" thick?
I would like to see the steps and how you approach this too...thanks Answered by Penny Nom. 





Digging a trench 
20090915 

From Darrell: In digging a pipe trench that measures 29 feet long, 2 feet 9 inches wide, and 3 feet 6
inches deep, how many cubic yards of earth were removed from the site? Answered by Penny Nom. 





The volume of a closed 3D mesh object 
20090910 

From Ozen: I want to calculate the volume of a closed 3D mesh object having a surface made up
triangles. Answered by Robert Dawson. 





The volume of a telephone pole 
20090811 

From robert: 12.5"@ base x 7" @ top and 40' height. How would I find the volume in cubic feet for a telephone pole with these dimensions? Answered by Harley Weston. 





The volume of a tapered pole 
20090809 

From robert: what is the formula to use to come up with cubic feet in a tapered pole Answered by Harley Weston. 





Torricelli's trumpet 
20090729 

From Gary: I was reading about torricelli's trumpet which is described by the equation1/x which is then rotated around the x axis which results in a figure which looks like a trumpet. Now in order to find the volume the integral 1/x^2 dx is used which diverges when integrated so the volume is finite.However if you integrate 1/x dx which is the formula on the plane the answer diverges. Now if you took an infinite area then rotated it around the x axis shouldn't you get an infinite volume? Notice the area I am talking about is under the line 1/x not the surface area of the trumpet which is what the painters paradox is about What am I missing? Thanks Answered by Robert Dawson. 





Sand for sandbags 
20090707 

From Jerry: How much sand do I need to fill 750 sandbags that are 26 inches by 14 inches if I fill them at 60% of their full capacity?nad Answered by Janice Cotcher. 





liquid in a 3/4 inch pipe 
20090630 

From junior: We are in dilemma at my job. We need to figure out the formula for how much water can our pipe hold. It's inside diameter is 13/16" and is 50ft. long? Answered by Robert Dawson. 





Cubic meters of gravel in a 7 ton lorry 
20090621 

From Jackie: I have to transport gravel in a 7 ton lorry and I know how many cubic meters of gravel I need, but I need to know how many cubic meters of gravel a 7 ton lorry can hold.
Thanks, Jackie Answered by Penny Nom. 





Maximum Volume of a Cylinder Inscribed in a Sphere 
20090618 

From Jim: Hello I have a hard time finishing this question:
A right circular cylinder has to be designed to sit inside a sphere of radius 6 meters
so that each top and bottom of the cylinder touches the sphere along its complete
circular edge. What are the dimensions of the cylinder of max volume and what is the volume? Answered by Janice Cotcher. 





Thermal Expansion of Steel 
20090617 

From Ken: Hi there, We are rollforming steel roofsheeting in 65M lengths and the =
question of linear expansion has cropped up.I would like to know what =
the expansion rate of this sheet would be over a temperature rise of say =
40degree F.in mm per Meter or whatever the norm is. The sheet is 0.53mm =
thick and is 700mm in width,I hope this is sufficient info to enable you =
to do your calculation.Many thanks, in anticipation.
Ken Answered by Janice Cotcher. 





Volume of a Can 
20090612 

From Zach: A can of soda has a volume of 355 mL. The area of a circle is given as A=pieR2, where r= radius of the circle. So, the volume of the can is given by V=(pier2)h, where h is the height of the can. If a particular can has a height of 12.2 cm what is the radius of the can?
I know the answer is 3.04 cm. I need help figuring out how to arrive at this answer what were the mathmatical steps?
Thanks,
Zach Answered by Stephen La Rocque. 





Cubic yards in an Irregular Shape 
20090608 

From ron: hi i have a berm 100'w x200'L at the base and 9'tall the top is 85'L x 20'w i would to find out how many cubic yards are in the pile and the formula Answered by Janice Cotcher. 





A border around a pool 
20090529 

From PATTY: POOL RADIUS IS 13 FEET ON THE OUTER EDGE, I WANT TO MAKE AN 18 INCH OUTSIDE BORDER AROUND THE POOL. WHAT IS THE VOLUME AROUND THE POOL. (THIS IS GOING FROM A 13 FT. RADIUS TO A 14.5 RADISU. Answered by Penny Nom. 





Formula for Volume and Weight of Water in Pipe 
20090514 

From Jonathan: Do you have a formula for the amount of water that would be in a 12" schedule
forty pipe in gal at any one time. The piping system will be under pressure
but I need to know the overall weight of a single 20' stick of pipe so that
I can determine my spacing for my concrete support inserts.
Thanks. Answered by Robert Dawson. 





Cubic Feet for Around a Pool 
20090514 

From Traci: I have a pool that is 24 ft round. I want to put a trim of 2 inch deep and 1 foot wide white rock around the outside. My problem is that here you can only purchase the rock in bags of either 0.5 cu ft or 1 cu ft.
How do I figure out how many bags i will need to do this right? Answered by Robert Dawson. 





The volume of an egg 
20090512 

From Dylan: What formula do you use to calculate the volume of an egg? Answered by Stephen La Rocque and Penny Nom. 





The volume of 3D figures 
20090429 

From Serena: What is the formula for finding the volume of 3D figures Answered by Robert Dawson. 





Volume of a prism 
20090421 

From David: The base of a rectangular prism has an area of 15.3 square inches and a volume of 185.13 cubic inches. Write an equation that can be used to find the height "h" of the prism Answered by Robert Dawson and Stephen La Rocque. 





The volume of a box 
20090415 

From Karen: Will 200 cubic centimeters of soil fit into the box?
8 CM by 6 CM and 4 CM deep Answered by Penny Nom. 





A toy pyramid 
20090403 

From Darah: Suppose you want to build a toy pyramid with a square base and a volume of 9000 cubic centimeters. What are the dimensions of a pyramid you might design? How many such pyramid designs are there? Answered by Stephen La Rocque. 





A large, hollow, ice cream cone 
20090403 

From Darah: A manufacturer is making a large, hollow, ice cream cone to serve as an ad for a local BaskinRobbins. The ice cream cone is made up of a cone with height 8 feet, topped by a hemisphere with radius 6 feet. How much ice cream could the hollow object hold? If a gallon is 0.13368 cubic feet, how many gallons does it hold? If 3 gallons of BaskinRobbins heavy cream chocolate blend weighs 24 pounds, how much would the ice cream cone weigh, excluding the weight of the construction material? Answered by Stephen La Rocque. 





The rate of change of the volume of a sphere 
20090325 

From Kaylin: why the rate of change of volume of a sphere is not constant even though dr/dt is constant? Answered by Walter Whiteley. 





The volume of a cylinder 
20090319 

From zahir: i want to ask one question, need i get the cross section of cylinder to calculate volume of cylinder Answered by Harley Weston. 





The ratio of the volumes of two cylinders 
20090318 

From jdkaj: cylinder a has radius 1m and height 4m. cylinder b has radius 2m and height 4m. find the ratio of the volue of cylinder a to the volume of b Answered by Penny Nom. 





The volume of water in a cone 
20090317 

From Freddie: A ball of diameter 20cm rests in a conical container whose angle with the slant height and the vertical axis is 25degrees. if water is poured into the container just enough to touch the bottom of the ball, find the quantity of water in the container. Answered by Penny Nom. 





How many bags do I need? 
20090316 

From Dawn: I need to purchase an item that is .4 cubic feet in size and the amount
I need is 5.625 cubic feet. How many bags do I need? Answered by Penny Nom. 





The volume of a pipe 
20090315 

From kalen: Okay I am doing a problem on a practice sheet to study with and I need help. The question states:
How many gallons will 500 feet of sixinch water pipe hold?
Do you have any suggestions/breakdowns on how to work out this problem so that in the future
I will know how to do it? Answered by Penny Nom. 





How many ball bearings can you make from a cone? 
20090314 

From Vatsal: there is a sum in my maths book which states the following:
how many ball bearings of diameter 2.5 cm. can you get by
melting a solid metalic cone of radi. 20cm and a Hight of 5 meters?
how do i do this please tell me even the minute things like cancellatoins and where to
use = , ; or any such thing because Im a bit weak in maths Answered by Harley Weston. 





Cubic feet 
20090307 

From A student: What is cubic feet and how do I use it in this question? (picture below) Answered by Stephen La Rocque. 





A rectangular prism 
20090225 

From Christina: I am trying to find the area of the base of a rectangular prism where one cube=_1 cu in. The Answer is given in square inches. I also need the volume of the prism in cu in. For example length=3, w=2, h=5 Answered by Penny Nom. 





Amount of Water 
20090223 

From Jeanette: I received a water bill for 660,000 gal. of water. I don't think it is possible to pass this much water through a 1 1/2 inch pipe in 30 days. Is it possible to send that much water? I am assuming that there is a water pressure of 50 gpm, but I am not sure of that. It is a rural water system. Answered by Janice Cotcher & Robert Dawson. 





Percentage difference in pipe volumes 
20090222 

From mike: what is the % difference between a 3 inch diameter pipe compared to a 4 inch diameter pipe? and how do i find the answer? Answered by Penny Nom. 





A ¾ inch copper pipe 
20090222 

From Ray: Hi
Do you have a formula I can use for this problem? And how to use it.
Thank You
How many feet of ¾ inch copper pipe will it take to hold 3 gallons of water? Answered by Harley Weston. 





Gallons of water in a 3 mile pipe 
20090219 

From tim: I need to know how many gallons of water a 16" pipe that is 3 miles long holds? Answered by Penny Nom. 





The volume of a cylinder 
20090218 

From jim: given the volume of a cylinder at 565m^3 and the height of 20m how do i calculate the cross section area in order to determine the compression strength of the cylinder Answered by Harley Weston. 





Tearing down a wooden privacy fence 
20090214 

From Dezra: we are tearing down a wooden privacy fence, it is 180' in length and
the boards are 4"w x 6' H=A0x 1" thick
i have a truck that holds 15 cubic yards. I would like to=A0know how many loads it's going to take to haul it off.
thank you for your help
dezra Answered by Harley Weston. 





A semi circular room 
20090211 

From Taylor: being 450pi (the area of a semi circle)
how much money would it cost to lay carpet at $2.57 per foot???
if the area of a semi circular room is 450 pi ft
then what is the volume being that the diameter is 60 feet
and the ceiling is 16 feet tall Answered by Robert Dawson and Penny Nom. 





Fertilizer in a bin 
20090203 

From Todd: Hello I am looking for a formula to figure out the fertilizer volume in a hopper bottom bin not only when it is full but part full as well. When you are filling it is heaped up in the middle to make a cone and when you are emptying the bin the cone is inverted so it would be nice to be able to quickly figure out the tonnes partly filled and when full.
Lets say the bin is 32 feet high from top of bin where you fill to the bottom where the product goes out and it is 16 feet in diameter. I know how to calculate the cylinder it is the cones on the top and bottom of the bin I have the main question on. Answered by Harley Weston. 





The amount of concrete in a football stand 
20090130 

From jacques: A football stand 150 yd long has 20 tiers of seats; each tier has a rise of 2ft and tread of 3ft.Its construction of reinforced concrete with a cross section as shown. Find the amount of the material used in its construction. Answered by Penny Nom. 





A railway cut 
20090130 

From Jean: A railway cut 200ft. long and 30ft. wide at the bottom is made with sloping sides, which are 80ft. and 60ft. in length. The 80ft. side is inclined 45 degrees and the other side is 35 degrees to the horizontal. Find the cost of removing the earth at $2 per load, if the trucks have capacity of 4cu. yd. Answered by Penny Nom. 





Shapes 
20090129 

From Rana: I want to know about Circumference / Area / Volume of different shapes ie Circle , Oval , An Arc Trapezide etc Answered by Robert Dawson and Harley Weston. 





A cubical tank that is 8 m on a side 
20090125 

From gina: Suppose one edge of a cubic tank is 8m; Find the volume of the tank in cubic meters Answered by Penny Nom. 





The number of gallons in a tank 
20090119 

From Jim: Hi, i need to know how many gallons of water can fit into our tank, and how to do the calculations my self. The tank is 72" round by 72" long, i would like some help. Thanks Jim. Answered by Harley Weston. 





The volume of a prism 
20090119 

From Mady: What is the general equation used to find the volume of a triangular prism? Answered by Robert Dawson and Harley Weston. 





20 miles of gasoline 
20090118 

From Roger: I used the volume formula and found that a cylinder with a 3" radius X 8.75" height yields just over 231 cu. in. (one gallon) doesn't seem right, but that's what I got. Then found the percent that 8.175" is to one foot and multiplied that into the number of feet in 20 miles. I'm not good at math, so I'm starting to lose myself here. The short story is I get a cylinder that is 20 miles long and only .0000387" in diameter. Is this even close to the mark? Answered by Harley Weston. 





Fuel in a tank 
20090116 

From Steve: I am not a math expert and want help seeing how much fuel is in a tank at one given time the tank that i have is 27 inches round. It is 69 inches long. laying length ways. it holds 140 gallons of fuel at fill up. I do know that it would hold less at the bottom of the tank an more in the center. Is there anybody that could just give me the figures by the inch without a formula. thanks for your time Answered by Stephen La Rocque. 





Concrete around a pipe 
20090114 

From Doug: How much concrete will i need for a hole that is 20 feet deep 20 inches in
diameter with a 8inch pipe in it. I need to know how much concrete
on the outside of the 8inch pipe. Answered by Penny Nom. 





The volume of a cone 
20090113 

From ab: the area of the base of the cone shown is 314 cm and it's height is 12 cam what is the volume? Answered by Penny Nom. 





The top half of a cone vs. the bottom half of the same cone 
20090108 

From Tammy: What is the ratio of the volume of the top half of a cone vs. the bottom half of the same cone? Is it seven times larger, or four times larger? and is the ratio consistent regardless of the size of the cone opening? Answered by Penny Nom. 





The volume and surface area of a sphere 
20090107 

From destini: the volume of a sphere is equal to its surface area. what is its radius Answered by Chris Fisher. 





Filling a round hole 
20090106 

From Kathy: I need to fill a hole that is 24 feet round x 12 inches deep. How much dirt will I need? Answered by Robert Dawson. 





The radius of a cone 
20090102 

From kalpaj: A conical funnel holds 100ml. If the height of the funnel is 10 cm, determine
its radius, to the nearest tenth of a centimeter. Answered by Penny Nom. 





The volume of a pipe elbow 
20081231 

From mhd: how i can find volume of the pipe elbow of 4inches? Answered by Stephen La Rocque. 





The base of a triangular pyramid 
20081220 

From joe: triangular pyramid
base height=
base width=8ft
height=6ft
volume=88ftcu.
Please explain base height & how to solve. Answered by Penny Nom. 





The volume of a feed hopper 
20081218 

From John: I need to calculate the volume of a feed hopper, and I'm not sure how to break it down. The top of the hopper is 36" x 36", it is 30" deep, and ends at a 6" x 6" plate. One side of the hopper is straight top to bottom, of course tapering on two sides to meet at the plate. The other three sides angle down at about 75 degrees. I need to determine the cubic foot volume of this hopper (it is used for ground coffee) so I can configure a vibrator to knock down residual grounds. Thanks. Answered by Robert Dawson. 





The volume of a pipe 
20081210 

From Walter: What is the volume of a pipe 7.92 inches inside diameter and 22 km. long in cubic feet of water Answered by Robert Dawson and Harley Weston. 





The cost of a foundation 
20081208 

From carl: Hi, I need to work out the cost of a foundation.
The foundation is 1m deep x 500mm wide and is 6.3 meters long.
The cost per cubic meter for concrete is 1000 rand
escuvation of earth will be 100 rand per cubic meter and back filling wil also be
100 rand per cubic meter.
What will the cost be Answered by Harley Weston. 





Ratio of Volumes of a Cylinder and a Cone 
20081206 

From rohan: A CYLINDER IS WITHIN THE CUBE TOUCHING ALL THE VERTICALS FACES . A CONE IS INSIDE THE CYLINDER.IF THEIR HEIGHT ARE SAME WITH SAME BASE ,FIND THE RATIO OF THEIR VOLUMES. Answered by Janice Cotcher. 





The volume of a yogurt pot 
20081204 

From Robyn: Okay, I know you have some answers on converting this already, but I can not convert the yoghurt pot I need yet into ml.
Is there some way to explain this using the yoghurt as an example?
The pot's 150g of lowfat strawberry yoghurt... would the 'lowfat' have an effect on this?
I'm sorry if this is a bother for you to answer, I just don't seem to be able to get it...
Have a nice day.
 Robyn Answered by Janice Cotcher and Penny Nom. 





The volume of a cone 
20081203 

From Tamriko: Hi! Help me, please to solve the following problem: The diameter of an icecream cone is 6 cm and the slant height is 10 cm. What volume of icecream would fit inside the cone? Thanks! Answered by Penny. 





A cereal box that has a volume of 12000cm^3 
20081124 

From William: Hi, I have this math question that says construct a ceral box that has a volume of 12000cm3 and the surface area of the box has to be between 3200cm2 and 400cm2, I found some dimensions that are 20 by 20 by 30 and it works, but when I attempt to make the box, or make a net I would need this hugh piece of paper/cardboard, which I don't have, is there an easier way to find different dimenshions so I dont need a hugh piece of paper to create a net easily? Because i've tried trial and error but it has taken to long and I cant find anything,else, thats resonable. Answered by Harley Weston. 





The volume is decreased by 25% 
20081117 

From Wanda: If the volume of a sphere is decreased by 25%, what is the new equation? Answered by Penny Nom. 





Two cubic yards, 4 inches deep 
20081115 

From Donna: How many square feet will 2 cubic yards cover if the depth is 4 inches? Answered by Stephen La Rocque. 





The volume of a cyclone 
20081113 

From Dianna: I need to figure the cubic yards of a cyclone. 144" down to 48" 60" high Answered by Penny Nom. 





A barrel on its side 
20081113 

From Dave: Question from Dave:
How many gallons are left in a 36x60 in. barrel (laying on its side) and has 16 in. of gasoline left. I have attached a diagram. Answered by Harley Weston. 





Liquid in a drum 
20081110 

From RAY: How can I determine the exact amount of liquid in an overturned drum? Answered by Penny Nom and Victoria West. 





The volume of a pond 
20081104 

From Malcolm: I am looking for a formula to find the volume of my pond. I know the average surface diameter and the average bottom arc length.(The arc from one bank through a point in the bottom and on to the surface on the other bank. I am not able to get a good measurement of the depth at this time. Can the volume be figured with the known measurements (the cord and the arc)? Thanks: MS Answered by Harley Weston. 





The height of a tank 
20081026 

From Kyle: If a water tank holds 750 cubic meters of water and it is 15 metres long and 10 metres wide how many meters tall is it ? Answered by Penny Nom. 





The amount of diesel fuel in a tank 
20081026 

From Mike: I have an cylinder shaped oil tank that holds approx. 283 gals of diesel fuel. The tank is laying on on its side, (like taking a garbage can and laying it down on its side). What is the formula to calculate how much oil is in the tank at any given time. If the tank was sitting on end it would be easy to figure out, but it is not. Answered by Stephen La Rocque. 





A football field covered in garbage 
20081017 

From AMie: a small city produces 500,000 cubic ft of garbage per week. If all of this garbage were stacked neatly (in a nice vertical pile) on a 100yard by 60yard football field, how high would the pile be (in feet)? Answered by Penny Nom. 





The volume of a slice from a wedge 
20081016 

From Jeff: If I have a wedge shaped object (ie, a triangle of nonspecific type
extruded along a length) and it is sliced from the twocorner base at
one end to the onepoint tip at the other, what is the volume of the
upper (smaller) part as a percentage of the whole? I hope I have
explained it clearly enough. Thanks. Answered by Harley Weston. 





The rate of change of the volume of a cone 
20081015 

From Barbara: Suppose that both the radius r and height h of a circular cone change at a rate of 2 cm/s.
How fast is the volume of the cone increasing when r = 10 and h = 20? Answered by Harley Weston. 





A cone shaped pile 
20081010 

From Nadine: I have a pile of wheat in the shape of a cone. I would like to know how much
wheat I have. I have found the equation "V=1/3 pie r squared h" , but it dosn't
work! The pile is 7 feet high, diameter is 50 feet, circumference is 185 feet.
I also measured the slope 19feet. (Probably not needed) You need to know that
wheat weighs 60 pounds per bushel, and I would like to know how many bushels
I have. Even if I could receive the # of Volume Bushels, I could convert that.
Can you help me?? Answered by Stephen La Rocque. 





Concrete around a pipe 
20081008 

From mick: i am trying to find the area of concrete to be placed around a concrete pipe! Dimensions can be 12m wide by 5m wide by 7m deep and pipe been 8m by 600mm radius... Answered by Stephen La Rocque. 





The length of a tank 
20081001 

From alex: I have a tank which I can only partly see. It is 70cms wide, 45 cm deep and hold 500litres. How long is it? Answered by Harley Weston. 





The weight of a concrete cylinder 
20080918 

From Curtis: I am trying to calculate the weight of a concrete cylinder. The diameter is 56" and the thickness or depth is 24". Can anyone help me? If possible I would like to see the formula as to how the answer was derived. Thank you Answered by Harley Weston. 





The volume of a cylinder in gallons 
20080917 

From subash: i want to calculate volume of cylinder tank whose height is 1700mm and
diameter is 1900mm and to convert volume into gallon ? Answered by Harley Weston. 





The volume of a box 
20080916 

From Andre: volume of the box cubic centimeters
____ X _____ X ______ X =_______
The length is 8.5 Width is 3.4 Answered by Penny Nom. 





An ice cream cone 
20080909 

From olivia: Judy has a sugar cone and wants to know how many cubic inches of ice cream it will hold if it is filled completely to the top of the cone and no more. The cone has a height of 4.5 inches and a radius of 1.5 inches. Answered by Penny Nom. 





The biggest right circular cone that can be inscribed in a sphere 
20080908 

From astrogirl: find the volume of the biggest right circular cone that can be inscribed in a sphere of radius a=3 Answered by Harley Weston. 





A circular swimming pool 
20080903 

From David: A circular swimming pool with a diameter of 30ft and a horizontal bottom contains 22,000 gal of water. What is the depth of the water in the pool? (one cubic foot contains approximately 7.5 gal of water.)
I'm having a great deal of problem dealing with this, i dont know if the equation I'm using is correct or am i plugging it in the wrong place. V=TTr^2h .
if you can could you please explain to me step by step on how to set up this problem? the horizontal bottom thrown me off the most Answered by Penny Nom. 





A rectangular tank of water 
20080902 

From Angela: A rectangular tank is 80 ft long, 30 ft wide, and 20 ft deep. If 100,000 gallons of water were pumped into the tank, what would be the water rise? Answered by Penny Nom. 





How many litres of rain is this? 
20080901 

From Todd: If i have 10mls of rain over one square metre how many litres would I
and how do I do the maths for this? Answered by Penny Nom. 





Trough Filling with Water 
20080821 

From lanny: a triangular trough is 10 feet long, 6 feet across the top, and 3 feet deep. if water flows at the rate of 12 cubic inches per minute, find how fast the surface is rising when the water is 6 inches deep. Answered by Janice Cotcher. 





The volume of a ditch 
20080812 

From John: Question from John:
I am trying to figure out how much flowfill I will need for a ditch that we are digging out. The ditch is 300' long and is 4' deep on one end and 2' deep on the other end. We are going to dig this ditch out and replace it with a flowfill concrete material. How much flowfill material will we need or what is going to be the volume of this ditch? Answered by Penny Nom. 





The volume of a swimming pool 
20080810 

From Ron: What is the volume of a swimming pool when its length is 40 ft, width 20ft, the deep end is 10 ft and the shallow end is 3 ft.? Answered by Penny Nom. 





A cubic mile of water 
20080803 

From Fred: [QQ] HOW MUCH WATER IS THERE IN A CUBIC MILE? Answered by Stephen La Rocque. 





The volume of a fuel tank 
20080801 

From G.: I have a fuel tank that is 70 inches by 48 inches and 24 inches deep, how many imperial gallons does it hold? Answered by Victoria West. 





Volume of a Shed 
20080724 

From lou: I need to know the interior volume in cubic feet of a shed with the dimensions 8' x 10' x 7' with a roof peak of 9'. Thanks Answered by Janice Cotcher. 





Constructing An Open Box 
20080723 

From Rita: An open box with a square base is needed to have a volume of 10 cubic feet.
(a) Express the amount A of material used to make such a box
as a function of the length x of a side of the square base.
(b) How much material is needed for a base 1 foot by 1 foot? Answered by Janice Cotcher. 





How much sand do I order? 
20080715 

From jackson: We would like to put 2 inches of sand down. The pool is 24 feet.
How much sand will we need?
The person we spoke to yesterday was talking in tons, but on these sites it is
talking cubic yards or feet.
Please help. We would like to get the sand ordered so we can get the pool up! Answered by Harley Weston. 





A silo with a flat side 
20080714 

From Amy: Without using the Pythagorean Theorem, determine the capacity of a silo in cubic feet of grain if: the cylindershaped silo has one flat, rectangular face that rests against the side of the barn; the height of the silo is 30 feet and the face resting against the barn is 10 feet wide; the barn is approximately 5 feet from the center of the silo. Answered by Harley Weston. 





The size of a pipe 
20080629 

From payal: hi , i want to know the area of a pipe with 63.5 mm diameter and 3718 mm height . can u pls help me Answered by Harley Weston. 





A concrete spectator area 
20080629 

From Paige: an area of the school courts is 58.5m x 60.4m,
The spectator area is to be 2m wide and the concrete has to be 10cm deep
Please can you calculate the volume of concrete needs for the spectator area? Answered by Penny Nom. 





How many gallons in an oval shaped tank? 
20080622 

From dale: how many gallons in an oval shaped tank, 72in long x46.5in wide x23in deep Answered by Penny Nom. 





A right prism with a square base 
20080613 

From Malik: Question from Malik:
A company wants to alter the dimension of container. The new container is in the shape of right prism equivalent to the current one.
The current container has height of 12cm and square base. The new container has also square base, but in the dimension base is increased by 3cm and height is decreased by 5cm.
if the cardboard is used to manufacture the new container, what area of cardboard is used to make new container? Answered by Penny Nom. 





How many yards of concrete will I need? 
20080612 

From Ron: I am putting up a flag pole, and I am trying to fiqure out how much concrete I need for the job. I have a round cardboard cement tube which is 18" across and 24" tall. The bottom of the tube will be filled with 3" of gravel and 3" of sand and the rest will be filled with concrete. Could you tell me how many yards of concrete I need. Answered by Harley Weston. 





The radius of a sphere if you know the volume 
20080611 

From Cey: how to i find the radius of a sphere with a volume of 1000cm cubed using the formula v=4/3 pi r squared???????/ Answered by Penny Nom. 





Packing a truck 
20080610 

From Ann: I am renting a 24ft box truck and have been told it is 1401 cubic feet. I want to know if I have 23 display cases to move and each is 6ft X 2ft X 3ft will the all fit? Or do I need additional info in order to figure this out? Answered by Penny Nom. 





Filling a hole with sand 
20080605 

From greg: I have a 18 ft. diameter circle and need to put 2 in. of sand in it i need to know how much sand in cubic yards and tons Answered by Harley Weston. 





The volume of a hexagonal pyramid 
20080605 

From Angie: My son is working on a hexagonal pyramid. The base is 4 and the slant height is 6. We know that the answer is 48 times the sqrt of 2. We don't know how they got it. We attached the drawing of it. Answered by Penny Nom. 





The volume of a solid 
20080604 

From Tom: The base of a certain solid is a circle of radius 2 while cross sections perpendicular to the
base are isosceles triangles of height 1. What is the volume of the solid? Answered by Harley Weston. 





I want to fill my backyard slope with fill dirt. 
20080525 

From Piero: I want to fill my backyard slope with fill dirt. The slope is 50 feet wide and the distance from the top of the top of the slope to the bottom is about 15 feet deep and the slope angle is at a 45. I want to know how many yards of dirt do I need to fill a space that is 20 feet out, 15 feet deep at a 45 degree angle. Answered by Stephen La Rocque. 





Find a way to represent the length and width of the box. 
20080525 

From Angela: The volume of a box that is two inches high can be represented by V=2X^220x+32. Find a way to represent the length and width of the box. (Hint: you will need to use factoring). Answered by Stephen La Rocque. 





Volume/weight of a salt shedweight 
20080521 

From James: How do I find the volume/weight of a salt shed. I have a 3000 ton barn, I need a better way of finding how much salt to order as it gets used. I know how to calculate volume, how do i get tonnage from there?? Answered by Harley Weston. 





A hemisphere and a cylinder 
20080518 

From Libby: A giant scoop, operated by a crane, is in the shape of a hemisphere of radius 24 inches. The scoop is filled with molten steel. The steel is then poured into a cylindrical storage tank with diameter 32 inches. How high will the molten steel rise?
I got the volume of the hemisphere and the volume of the cylinder, but I'm not exactly sure what to do next. Answered by Penny Nom. 





Tyres in a shipping container 
20080514 

From Carlene: I need to work out how many tyres will go in a shipping container.
The shipping container is 10 foot long, 8 foot wide and 8.6 foot high.
The tyre is 175 millimeters across and it is 14 inches in tyre thickness.
How many tyres will fit in my container? Answered by Stephen La Rocque. 





The weight of a concrete column 
20080511 

From russell: a cylindrical form is filled with a slow curing concrete. The base of the form
is 10 ft in radius, and height is 25 ft. while the concrete hardens, gravity
causes the density to vary from a density of 90 lbs/ft^3 at the bottom to a
density of 50 lb/ft^3 at the top. Assume that the density varies linearly
from the top to the bottom, and compute the total weight of the resulting
concrete column Answered by Harley Weston. 





The volume of a ditch 
20080509 

From Dixie: I need to find the cubic feet of a ditch 36 inches wide by 28 inches high, by 1561 feet long.
then I need to convert it to cubic yards then to tons. of rock Answered by Penny Nom. 





A bowl is the shape of a hemisphere 
20080428 

From josh: a bowl is the shape of a hemisphere with diameter 30 cm and water is poured into the bowl to a height h cm. how do i find the volume of the water in the bowl Answered by Harley Weston. 





A volume of revolution 
20080424 

From Sabahat: Hi, i have a region enclosed by both axes, the line x=2 and the curve y=1/8 x2 + 2 is rotated about the yaxis to form a solid . How can i find the volume of this solid?. (Please note that y equation is read as y =1 over 8 times x square plus 2.) I will be really grateful if you answer this question. :) Answered by Harley Weston. 





The isoperimetric inequality 
20080421 

From Dutch: I'm searching for the proof that the sphere has the smallest volume of any figure and maximizes the volume of any figure. Answered by Chris Fisher. 





The volume of a stone 
20080417 

From sara: a rectangular tank 30 cm long and 20 cm wide is filled with water to a depth of 8 cm. When a stone was put in, the water level rose to 11 cm. Find the volume of the stone. (Assume that the stone is completely under water.) Answered by Penny Nom. 





The capacity of a silo 
20080412 

From Candonn: I have a cement silo that is 30 ft. high and has a diameter of 12 ft.
I was wondering what the capacity of the silo is in tons of dry material.
The silo is flat on the bottom also. Answered by Penny Nom. 





A truncated cone 
20080411 

From jason: i need to know how to figure the cubic feet of a cone that the top is 72" wide the bottom is 25" wide and it is 48" tall.
is there a specific formula for this? Answered by Penny Nom. 





The volume of a triangular shaped pond 
20080410 

From Bret: we have a pond that is triangular shape : 130ftx130ftx150ft and is 4ft deep. How can I figure out as to how many gallons of water it will take to fill it up? Thanks for your help :) Answered by Penny Nom. 





How many bags of mulch? 
20080407 

From MJ: I have an area that is 35' X 50' and I want to cover it with 2" of mulch.
Do I take length X Width X depth? Bags of mulch are sold in 2 or 3 cubic feet per bag.....I just want to know how
to do the math. can you please send me the equation? Answered by Penny Nom. 





The amount of a washing machine 
20080407 

From Eddy: we have a washing machine with a specific cylinder size, which we could calculate the volume as a regular cylinder formulas. The question is, if we fill the washer cylinder with water at a specific height on water , example 15 cm height, how can we find the volume of water at that specific height? Answered by Penny Nom. 





A volume of revolution 
20080404 

From ted: Consider the region bounded by y=x^2 + 1, y=53x and y=5. Sketch and
shade the given region; then set up but dont evaluate teh integrals to find
the following:
a) The volume of the solid generated by rotating the region about the line
y=5
b) the volume of the solid generated by rotating the region about the yaxis Answered by Penny Nom. 





810 slabs of concrete 
20080401 

From Wesley: I'm making a 4" x 4" x 2" (Inches) concrete slab (approximately 750 of them, I'm going to plan for 810 for extra material). I'm trying to find out how many bags of cement I need. Each 60 lbs bag makes approximately .5 cu/ft. Answered by Harley Weston. 





I have to fill a hole with clay 
20080331 

From Tim: Dear Sirs I have to fill a hole with clay and then 8 inches of top soil. The area is a 24 foot circular hole left by a now removed swimming pool. The area in question pithces from the house from 48" to ground level within that 24 feet. I was wondering how many yards o the top soil has to be 58 inches deep thank you f fill(clay) I would need and how many Yards of top soil to cover that hole Answered by Harley Weston. 





How many bags of cement do I need 
20080330 

From Joe: How many bags of cement do I need if I want to extend my carport 6 inches all around?
The carport is 15ft. x 15ft. and the existing slab is 4 inches thick. Answered by Harley Weston. 





A car tire full of concrete 
20080327 

From robert: I want to build a volleyball net support. I am using a car tire 24"odx16"id filled with concrete. how much will this weigh? thanks Answered by Penny Nom. 





The volume of a footing 
20080323 

From Brett: You need to pour an 8"x16" footing that is 100ft. long. At a cost of
$65 per cubic yard, how much will this cost?
(A) $205 or less
(B) more than $205, but less than $220
(C) $220 to $235
(D) more than $235 Answered by Penny Nom. 





The volume of a dam 
20080323 

From JD: How many cubic yards of soil are required to build a small Pond Dam:
100ft wide bottom x 300ft long x 15ft High with a 14ft wide Flat top Answered by Harley Weston. 





Determine the capacity of Farmer John's silo 
20080316 

From paula: Farmer John stores grain in a large silo located at the edge of his farm. The cylindershaped silo has one flat, rectangular face that rests against the side of his barn. The height of the silo is 30 feet and the face resting against the barn is 10 feet wide. If the barn is approximately 5 feet from the center of the silo, determine the capacity of Farmer John’s silo in cubic feet of grain. Answered by Penny Nom. 





The volume of a countertop 
20080308 

From Matthew: I need to calculate volume down to cubic feet. I pour concrete countertops
and cant figure out the formula to convert inches and feet. If I have a 2.5 inch
by 2 foot by 16 foot concrete countertop how do I convert it to cubic feet
and hence know how many bags of concrete at .6 cubic feet per bag I will need.
I am trying to input the formula into a spreadsheet. thank you so much Matt Answered by Penny Nom. 





The volume of a cereal box 
20080303 

From Lawson: I have calculated the volume of a box of cereal whose dimensions are:
Length  19 cm
Width  3 cm
Height  27 cm
I need help with the follow question:
If 2cm3 = 30 pieces of your cereal, how many pieces of cereal will fit in your box? What do I do the calculate? Answered by Penny Nom. 





The volume of a truncated prism 
20080303 

From jhey: The volume of a truncated prism is 6240 cu cm. The base is a right section in the form of an equilateral triangle. The edges perpendicular to the base are 15 cm, 18 cm, and 15 cm long. Find the length of one side of the base. Answered by Harley Weston. 





Pea gravel 
20080224 

From Linda: I have a space of 16 feet by 8 feet. I want to fill it with pea gravel 6 inches deep. If the bags of pea gravel are
.53 cubic foot. How many bags would I need. Thanks so much. Answered by Stephen La Rocque. 





The volume of a pyramid 
20080203 

From Britni: The base of this pyramid is an equilateral triangle with sides 8 units.
The altitude of the pyramid is square root of 3. What is its volume? Answered by Penny Nom. 





Volume of a log 
20080129 

From Reji: i purchased a teak wood length 20feet and perimeter 60inch. How much cubic feet will be the wood. Answered by Stephen La Rocque. 





Belledout pier 
20080128 

From Gina: I need to know how to find the total yards needed to fill a concrete pier that is 54"/ 108" and 26' deep.
That is...54" @ the top of the pier belled to 108" @ the bottom...26' deep. Answered by Stephen La Rocque. 





The volume of a tank 
20080127 

From Fred: A cubic tank holds 1,000 kilograms of water what are the dimensions of the tank in meters? Answered by Harley Weston. 





Maximum volume of a box 
20080115 

From Rajesh: A square piece of a cardboard of sides ten inches has four equal peices are removed at the corners, then the sides are turned up to form an open box. What is the maximum volume such a box can have? Answered by Stephen La Rocque. 





Constructing a pool 
20080115 

From Scott: what it the cubic yards needed for this pool.
It is 14ft. X 28ft. and 6 inches thick. It is 3.5ft. deep on the shallow end and 6ft. deep at the deep end. Answered by Stephen La Rocque. 





How many bags of cement will I need? 
20080115 

From James: I want to extend my front porshe more to the left atleast 14' 1" length wise and 5' 1" width wise with 4" thickness. Now i already decimalized in feet those inches, resulting with 14.08 length and 5.08width and 0.33 of thickness. I then Get my square feet of 71.53. And go on to cubic feet getting a 23.60 in cubic feet. Now i want to convert to cubic yards so i then divide 23.60 into 27 and get 0.87. Now my question is how would i use this to go and buy the necessary bags of cement knowing that a 94 lb. bag of cement is 1 cubic foot of bulk material. To fill 4 inch of thickness and 14' of length and 5 of width? Answered by Stephen La Rocque. 





What length of hose will I need? 
20080103 

From Justin: I have one cubic yard of liquid that I want to convert to a cylindrical volume with the inside dimensions being 3/4 of an inch. I am trying determine what the height/length would be to set these equal. i.e. What length of hose will I need (with an inside diameter of 3/4") in order to accommodate exactly one cubic yard of liquid? Answered by Penny Nom. 





Volume in cubic feet 
20071220 

From kim: if i have the inches and need to convert them to cubic feet, how do i do that? i thought it was height X width X length. Answered by Penny Nom. 





A 300 ton train locomotive is built at exact half scale in all dimensions 
20071216 

From Normand: When a 300 ton train locomotive is built at exact half scale in all dimensions
we assumed the weight would be 150 tons.
Like a bar of solid steel cut in half would be.
Why does this not work out?
What are we missing here? Answered by Penny Nom. 





Bags of concrete 
20071206 

From Chris: I need 1 and one half yards of concrete for a project. If one bag is equal
to 0.38 cubic feet, how many bags will I need? Answered by Penny Nom. 





Ball bearings in an oil can 
20071203 

From Lisa: One hundred ball bearings with radius 5 mm are dropped into a cylindrical can, which is half full of oil.
The height of the cylinder is 20 cm and the radius is 8 cm.
By how much does the level of the oil rise? Answered by Stephen La Rocque. 





Will the container hold all the liquid? 
20071126 

From john: a bottle contains 750 ml of oil. the oil is poured into a container 12 cm high and with a square base of side 10cm.
(a) will the container hold all the liquid
(b) if the answer to (a) is 'no', how much liquid will be spilt?
(c) if the answer to (a) is 'yes', how much more liquid will the container hold? Answered by Leeanne Boehm. 





The volume of a soccer ball 
20071125 

From Ria: A student of me is working on a paper about soccer and math/physics. He wants to calculate the volume of the ball, which is composed of 5 and 6sided pyramids. We are looking after a formula to express the volume of these pyramids in function of the radius of the ball (and if possible how we can derive this formula). Afterwards we'll try to calculate the difference with the volume of a sphere with radius r. Answered by Stephen La Rocque. 





A cylindrical tank 
20071116 

From Mario: I want to determine how many gallons i have inside a cylinder (tank) that is resting on its side (the Height), NOT standing up.
I know V=pi x r2 x H. And 1 cubic foot = 7.48 gallons. Here are the dimensions r=2' H=20'. Now my question is how do I determine how much
liquid i have inside, if the level of the liquid is about 1/2 of the way of its Diameter (in other words 2'). Remember this cylinder is lying
on its side. Answered by Penny Nom. 





Changing units and sizes of things 
20071108 

From Carol: volume of cube = 216 cubic inches how do I calculate cubic feet and calculate its surface area in square feet.
a rectangular box has dimensions of 3 x 6 x 15 how do I calculate surface area in square yards and calculate volume in cubic inches. if I double the dimensions how does it affect the volume Answered by Stephen La Rocque. 





The volume of a vial 
20071106 

From Derrick: An empty vial has a mass of 65.92 g. If the vial has a mass of 202.91 g when completely filled with liquid carbon terachloride (d = 1.59 g/cm3), what is the volume of the vial? I have tried several solutions but none i can come up with seem to be correct. Answered by Penny Nom. 





How many cubic yards of dirt do I need? 
20071016 

From BELINDA: I need to fill an area of 30,000 square feet with dirt that is 18" in height. How many cubic yards of dirt do I need to do this? Answered by Penny Nom. 





How much water is in a hose? 
20071012 

From Bryan: I need to know how much water (gal) is in a hose thats 100' long by 5" in dia.
Thanks Answered by Stephen La Rocque. 





The amount of dirt 5 feet deep over a 50 acres 
20071002 

From Debbie: Please tell me how to calculate the amount of dirt stripped 5 feet
deep over a 50 acre site. How do you calculate the amount of dirt in an acre
and then excavating it a certain depth. How does one calculate the amount of
dirt excavated and moved and how to price to charge for the service? Answered by Stephen La Rocque and Victoria West. 





Oil in a pipe 
20070929 

From Kristi: How much oil is in a 40 foot section of pipe that its inside diameter is 36 inches? Answered by Victoria West. 





How much water to fill my bedroom? 
20070922 

From hector: how can i find out how much water i can fill my bedroom with when it measures 12 ft.x12 ft.x10 ft. Answered by Steve La Rocque and Penny Nom. 





Filling a planting bed 
20070918 

From Luke: How many 40lbs bags will it take to fill area 21feet long 45inchs wide 9 inch deep? Answered by Penny Nom. 





Volume of a cylinder 
20070915 

From mike: I need to know the formula to measure conceret celinders Answered by Penny Nom. 





Volume, mass and density 
20070914 

From Nathan: I have a sample of material that is 10cmx10cmx5cm and has a mass of 29 grams. How many grams would a sample of the same material that was 96cmx188cmx5cm be? Answered by Penny Nom. 





How much stone will be needed to fill the trench? 
20070914 

From Debbie: A trench 100metres long 1ft wide*18inches deep with a 4inch pipe laid. How much stone will be needed to fill the trench.
How much weight in stone would I need to fill it? Answered by Penny Nom and Victoria West. 





Is it platinum or silver? 
20070914 

From Jordan: In Chemistry we are doing a lot of problems that are much more math related than anything. One of my questions reads: A certain medallion has a mass of 55.64 g. When placed in 75.2 mL of water in a graduated cylinder,
the water level rises and then reads 77.8 mL.
Is the medallion made of platinum (D=21.4 g/mL) or silver (D= 10.5 g/mL)? Answered by Penny Nom. 





The contents of a silo 
20070914 

From Steven: I need to know how to find the weight of the contents of a silo that is 4 feet across and is funnel shaped at 60 degrees Answered by Penny Nom. 





How much space we are talking about when they say 500 cf? 
20070911 

From Rhonda: I was informed while planning a move that the moving company will
allow 500 cubic feet of moving space. Anything over that is $5.99 per cf.
How do I find out exactly how much space we are talking about when
they say 500 cf ?? Thankyou in advance for the advice. Answered by Stephen la Rocque. 





Water in a conical tank 
20070910 

From Greg: Joe is conducting an experiment to study the rate of flow of water from a conical tank.
The dimensions of the conical tank are:
Radius at the initial water level = 13.7 cm
Radius at the reference point = 12.8 cm
Initially the tank is full of water. There is a circular orifice at the bottom of the conical
tank with a diameter of 0.635 cm. The water drains from the conical tank into an empty
cylindrical tank lying on its side with a radius of 0.500 ft and a length L (ft).
Joe observed the water discharged with an average velocity of 1.50 m/s as the water level
lowered from the initial height of 14.0 cm to 5.00 cm in the conical tank. Answer the
following:
1. If the initial height of water in the conical tank is 14.0 cm (measured from the
reference point, see Fig. 1), how long in seconds will it take for the water level to drain to
a height of 5.00 cm?? NOTE: Height refers to the vertical height.
What formula would I use to find out how long in seconds it takes for the water level to drop? Answered by Harley Weston. 





Two inches of topsoil 
20070910 

From Nick: I have to cover a 5,300 square feet area with topsoil 2" deep. How many yards would I need? Answered by Harley Weston. 





Liquid in a pipe 
20070905 

From christian: how many cubic feet are in a pipe that is 3" (inside diameter) and 459 feet long? Answered by Stephen la Rocque. 





A turtle tank 
20070830 

From Natasha: I have a tub that we are going to use for a turtle tank. it is 3 feet long 1foot 7in wide and 1foot 5 in deep. how many us gallons will this tub hold? Answered by Harley Weston. 





Filling an old swimming pool 
20070827 

From Russ: I would like to know how much fill material I would need to fill an old swimming pool. The pool is 18' wide x 36' long and is 4' to 10' deep. Answered by Penny Nom. 





A frustum of a right pyramid 
20070824 

From Andrew: Find the volume of a frustum of a right pyramid whose lower base is a square with a side 5 in., whose upper base is a square with a side 3in., and whose altitude is 12 in. Round your answer to the nearest whole number.
A. 47cu in. C. 226 cu in.
B. 196 cu in. D. 1036 cu in. Answered by Stephen la Rocque. 





I want to fill the hole up with dirt 
20070819 

From Roger: I have an 18 foot round hole which is 16 inches deep. I want to fill the hole up with dirt. How much dirt do I need to fill the hole?? Answered by Penny Nom. 





How much water is this? 
20070816 

From Judy: Have an area 731 sq. ft with 5" of water all the way around. How many gallons is this? Your help is appreciated. Answered by Stephen La Rocque. 





How do I find out how much cubic meters will spread over meter squared area? 
20070816 

From Derek: How do I find out how much cubic meters will spread over meter squared area? Answered by Penny Nom. 





Water bill woes 
20070812 

From Terry: I know that a cubic foot of water=7.48051945 gals., but I keep getting my water bill and they go by thousands of a gal. per cubic foot. Is there a conversion that says that shows this? Water department=.763 x cubic foot used=thousands of gallons water used that month. Exampel: 72cu. ft meter reading x .763+ 58. galons of water I use in a month. Total 58=thousand = +gallons. This is wrong. There are only two people in the house. Answered by Stephen La Rocque. 





Scalar triple product and volume of a general tetrahedron 
20070803 

From Anurag: how do you prove that
volume of tetrahedron= 1/12 times scalar triple product of vectors a,b and c? Answered by Stephen La Rocque. 





A gas tank 
20070801 

From Randy: I am trying to determine the size of the gas tank on a used truck I just purchased. There is no tag on it showing the size. It measures 50" wide by 12" high by 18" deep. How many gallons of gas does it hold? Answered by Penny Nom. 





An irrigation ditch 
20070731 

From Kevin: I would like to know how many cubic yards of concrete I would need to fill a section of irrigation ditch that measures 12 inches on the bottom, 40 inches on top, 16 inches high and 20 feet long with a 18 inch diameter, 20 foot long culvert sitting in the ditch (to remain open). I am trying to build a roadway across the irrigation ditch. Thanks very much. Answered by Penny Nom. 





A 20,000 gallon fuel bag 
20070728 

From Kevin: I have a 20,000 gallon fuel bag Length 32'x Width 29'x Height 4.2'. I need to build a containment around it. If the bag was to rupture the containment would have to hold the 20,000 gallons of fuel plus ten percent. What size would the containment have to be in order to hold the fuel. Answered by Stephen La Rocque. 





A football stand 
20070719 

From jean: a football stand 150 yd. long has 20 tiers of seats; each has a rise of 2 ft. and tread of 3 ft. it constructed of reinforced concrete with a cross section of 36*54. find the amount of material used in its construction. Answered by Harley Weston. 





The volume of a cistern 
20070719 

From sharon: We have a cistern to hold spring water that measures 12 feet in depth by 5 feet in diameter. How much in liquid gallons will it hold? Answered by Penny Nom. 





A triangular trough 
20070719 

From janine: A trough is formed by nailing together, edge to edge, two boards 11 ft. in length, so that the right section is a right triangle. If a 15 gallon of water are poured into the trough and if the trough is held level so that a right section of water is an isosceles right triangle, how deep is the water? (231cu.in=1 gal.) Answered by Penny Nom. 





I need to provide 712 cubic feet to water storage capacity 
20070703 

From William: I need to provide 712 cubic feet to water storage capacity.
If I use 15 inch diameter pipe, what would the length need to be
to provide the capacity? Answered by Stephen La Rocque. 





A sand base for a pool 
20070701 

From Clark: I am adding sand for a base for a pool. It is 20' round and I would like the sand
to be 2" deep. Can you tell me how many cubic feet that would be?
Thanks! Answered by Harley Weston. 





A cylindrical slab of concrete 
20070630 

From Kenn: I have a tank that needs a base of cement put in it. I dont know how to do this. The tank is 8 feet across and I want the cement to be 5 or 6 inches deep. Can you please tell me how much cement I need to do this. Answered by Harley Weston. 





A cubic yard of gravel 
20070624 

From Duncan: I'm trying to figure out how much area 1 cubic yard of gravel would cover at a depth of 2 inches? I've asked around and have many different answers. Answered by Stephen La Rocque. 





Volume in a triangular water trough 
20070624 

From David: A water trough has sloping sides of length 500mm making it triangular in cross section, with vertical ends. The width at the top is 600mm and the length is 2.0 metres.
(i) Calculate the capacity of the trough, giving your answer accurate to the nearest litre.
(ii) Find out the depth of the water when the trough is half full. Answered by Stephen La Rocque. 





The volume of a cube 
20070623 

From Leah: I am having trouble finding the equation for this problem.:
What is the volume of a cube with diagonals of length 6 sqrt(3) cm?
answer: (BLANK) cm3 Answered by Penny Nom. 





Volume of a box 
20070622 

From ashley: A storage bin is 18 ft long, 6 ft wide and 3 ft high. What is its volume in cubic feet? Answered by Penny Nom. 





Making a box with a particular volume 
20070620 

From Kimberly: How do you convert 487 cf into box? Answered by Stephen La Rocque. 





The volume of a pool 
20070620 

From Mary: How can I calculate the square footage of my 18 feet diameter, 4 feet deep swimming pool? Answered by Penny Nom. 





How many gallons of water 
20070619 

From Marie: A water treatment plant is built with three cylindrical tanks to contaim the
water for a town. Each tank has a radius of 15 feet and a depth of 25 ft.
If there are about 7.5 gallons in a cubic foot of water, approximately
how many gallons of water can be treated at the plant at any one time? Answered by Stephen La Rocque. 





How many tons of sand? 
20070619 

From Richard: I need to know how many tons of sand it would take to fill a container 20 feet
long, 20 feet wide, and 6 inches deep. I am not sure of the makeup of the sand as
far as dry, loose, wet, etc. If you could give me calculations of all the variants it
would be appreciated. Answered by Stephen La Rocque and Penny Nom. 





A pipe full of water 
20070607 

From paul: What is the volume of water in a 100mm inside diameter pipe that is 12.5 meters long
What would be the pressure at the bottom if the pipe was installed in the vertical plain Answered by Steve La Rocque, Penny Nom and Gabriel Potter. 





Yards of top soil 
20070606 

From Cristina: How many yards of top soil do I need in a area of 2000 square feet with 18" depth. Answered by Penny Nom. 





Volume of a brewer's sphere 
20070604 

From Edward: A Brewer's Sphere that has a 9' Dia. Holds how much Brew? How many 40oz bottles will be needed to hold his batch of Brew? Answered by Stephen La Rocque. 





The volume of a triangular prism 
20070601 

From Hannah: How do I find the area of the base of a triangular prism, so that I can find the volume by using the equation on the attachment. The formula is that volume equals one half times (base times height) times triangle height. Thank you for your help.
Hannah Answered by Penny Nom. 





Water tank volume 
20070529 

From Cecelia: I HAVE A SEMI CIRCULAR TANK AGAINST A WALL MEASURING 6'10" ACROSS THE WIDEST PART AND 3' FROM THE WALL TO THE FRONT OF THE TANK. THE DEPTH IS 14". PLEASE HELP ME TO CALCULATE THE VOLUME OF WATER IN THE TANK. Answered by Stephen La Rocque. 





Volumes of cones and cylinders 
20070529 

From George: 1. The volume of a cylinder is 1353cm3
A) What is the volume of a cone with the same radius as the cylinder
but double the hieght of cylinder?
B) What is the volume of a cone with the same height as the cylinder
but with three times its radius? Answered by Steve La Rocque and Walter Whiteley. 





Volume of a chest 
20070524 

From Jerry: Heighth: 28" Width: 32" Depth: 20" Answered by Stephen La Rocque. 





Mulch price comparison (price per cubic yard versus price per cubic foot) 
20070523 

From Dianna: This is a 2fold question. I am getting some mulch that is measured in 1 cubic yard for $25.00.
Walmart has a 2 cubic bag for $3.00. I need to cover a 376 sq ft area. I need to know which is
the best deal and how much I need to buy to cover the 376 sq ft. Answered by Stephen La Rocque. 





How many tons of dirt is this? 
20070523 

From Deb: I need to know how many tons of dirt(6 inches deep)would it take to cover 8 acres? Answered by Stephen La Rocque. 





Converting mass of sand to volume (a sand ceremony) 
20070521 

From Linda: I'm getting married. We are having a sand ceremony. The empty bottle we are using holds 800ml. I have bags of colored sand. Each bag is 30g. There is 7 people participating in this ceremony. What I need to find out is how many grams of sand i need for 7 people to participate to fill this jar. Answered by Penny Nom. 





Constant rate of sand falling in a cone 
20070520 

From Nhi: Sand is falling into a conical pile . After 5 min. the pile has radius 24 and height 26 . After 7 min. tell how far the point c. is from the top of the cone (A). Answered by Stephen La Rocque. 





Cost of replacing a driveway 
20070517 

From Chris: A homeowner needs to replace a driveay which is 12 feet wide and 90 feet long. The old driveway needs to be dug out. It is 9 inches deep. It costs $35 per cubic yard to remove the old driveway and $75 per cubic yard to lay the new one. What will be the cost of the complete job? Answered by Penny Nom. 





Buying topsoil 
20070516 

From Claudia: I am trying to figure out if it is cheaper to buy topsoil by the bag (one 40lbs bag for $1.66) or having it delivered for $60 for 4 cubic yards. Answered by Penny Nom. 





Volume of a wedge 
20070514 

From Mark: We need to fill in dirt along a 75 foot long fence, 3 feet out , statring at 6 inches agaisnt the fence, sloping to 2 inches at the grass. I am trying to calculate the volume to order enough cubic yards of dirt to fill this. Answered by Stephen La Rocque. 





Maximizing the volume of a cone given the slant length 
20070514 

From Christina: A coffee filter for a new coffee maker is to be designed using a conical filter. The filter is to be made from a circle of radius 10cm with a sector cut from it such that the volume of coffee held in the filter is maximised. Determine the dimensions of the filter such that the volume is maximised. Answered by Stephen La Rocque and Kerstin Voigt. 





Prealgebra volume of a prism 
20070510 

From Brenda: Find the volume of a triangular prism with a base of 5 cm by 5 cm and a height of 12.5 cm. Round to the nearest tenth. Answered by Stephen La Rocque. 





Cubic feet of sand 
20070509 

From Paul: I have an above ground pool that is 585 sq feet. I want to cover the bottom in 3 inches of sand. The sand supplier says I need about 6 cubic yards, based on your prior answers on this subject. I come up with 1.8 yards. What is the correct amount? Answered by Stephen La Rocque. 





A speaker box 
20070505 

From darell: I am trying to build a speaker box, and i am trying to find out the measurements of a 1.5cubic feet box. Answered by Penny Nom. 





Edging surrounding a round pool 
20070503 

From Carol: Hello,
I am new at this and very rusty on my math. I am getting a 24 Ft. round pool and would like to put 2ft width stone (small) edging around it. How much would I need to buy. I have to buy it by the yard (cubic yard) I am not looking for an exact, just an approx. even would be great.
Thanks
Carol Answered by Stephen La Rocque. 





How many tons of sand is needed 
20070425 

From Jennifer: How many tons of sand is needed to cover 350 cubic square feet? Answered by Penny Nom. 





How much water is in the pool 
20070423 

From Kayla: how much water is in a pool which is 10m x 5m and is 1.5m to 2.5m in depth? Answered by Penny Nom. 





The size of a freezer 
20070423 

From Jacqui: How many can packages can fit? I have a freezer that is 7cf. But
it contains a little tray component. The freezer measurements without the
tray is(bear with me, I'm not good with LxWxD) 23 across x 16 W x 25
deep (I'm assuming depth) and the tray is 8 across x 16 w x 15 D. We are
trying to see how many 9 L x 6 W x 3.5 D packages can fit in the freezer.
Please help me. I'm getting app. 60. I need 84 to be able to fit. Answered by Penny Nom. 





A bag of mulch 
20070422 

From John: I have a bag of mulch that contains two cubic feet of mulch. If I speard it out at a height of one inch, in a three foot wide flower bed  how feet can I cover? Answered by Stephen La Rocque. 





Relating volume to depth in a cylindrical container 
20070419 

From Dan: I have a cylindrical polyethylene rain barrel 23" in diameter and 35" high. If I've calculated correctly thus far, its volume is:
14, 547.49 cubic inches (or 8.418686 cubic feet or 0.31 cubic yards)
and could, ideally, contain 62.6 gallons of rain water whose weight would be 525.32 lbs. (62.4 lbs./cubic foot X 8.418686).
I'm having difficulty relating inch depth markings on the side of the barrel to volume capacity; i.e., how many inches in depth
in a cylinder of the size given would = how many gallons (or quarts) of water. The barrel stands upright on its end and is, thus, 35" high
when oriented in this fashion, much as a 55gallon oil drum appears when similarly stowed.
Dan Watley Answered by Stephen La Rocque. 





Swimming pool water 
20070412 

From tina: How much water does a 24' round, 4' deep swimming pool hold? Answered by Haley Ess. 





A volume of revolution 
20070408 

From christina: find the volume of the solid formed when region bounded by y=x/3, y=2
and the yaxis. it is revolved about the xaxis.
the assignment was to use both the washer method and the shell method
but when i solved for the volume, i got different answers.
i think my shell method is wrong because i know i'm having difficulties
with using "dy" instead of "dx"
here's my work so far: Answered by Penny Nom. 





Find the volume of the solid 
20070407 

From tricia: a solid is constructed so that it has a circular base of radius r centimeters
and every plane section perpendicular to a certain diameter of the base is
a square, with a side of the square being a chord of the circle.
find the volume of the solid
at first i thought the length of a side of the square would be r, but that
isn't awlays be true only when the chord is in the center.
so how can i solve this without any values? i dont understand the relationship
between the chord and radius, except that the radius intercepts
the chord at the midpoint.
i know i hav to take the integral to get the volume,
but how do i even find the area of one of the squares?
please help,
thanks,
tricia Answered by Penny Nom. 





A pipe with 8 inch inside diameter and ten feet long 
20070403 

From Frank: How many cubit feet are there in a pipe with 8 inch inside diameter and ten feet long.
Thank you Answered by Stephen La Rocque. 





How much gravel do I need 
20070331 

From linda: how much gravel do I need for 254 square feet to be 4 inches deep? Answered by Penny Nom. 





How many tons it will take to fill in this area 
20070329 

From Amy: I have to fill an area with millings (crushed stone). The measurements are 14 foot long, 14 foot wide, and a depth of 6 inches. How do I find the square footage and how do I convert that into tons?
I need to know how many tons it will take to fill in this area. Answered by Penny Nom. 





How many yards of gravel do I need? 
20070328 

From Joel: I am constructing a French drain 100 feet long x 6 inches wide by 18 inches deep. Within this trench will be a 4" diameter pipe which will be surrounded by washed gravel. How many yards of gravel do I need? Thanks! Answered by Stephen La Rocque. 





The volume of a cylinder 
20070328 

From bob: how do you find the volume of a cylinder that is 12 centimeters wide and 16 centimeters tall? Answered by Penny Nom. 





The volume of a trough 
20070327 

From Tracy: I need help trying to find the volume of a 9 ft long trough that has two
equilateral triangles on the end. When the water of the trough is 2 feet
deep and its depth keeps increasing by 1/2 ft/minute. I have to figure
out at what rate the water is flowing into the trough.
Can you point me in the right direction for finding the equation
for the volume of the trough? Answered by Penny Nom. 





Painting a pool 
20070325 

From vincent: Determine the total cost to put 2 coats of paint on the interior pool
and amount of water needed to fill pool
facts:
a gallon of paint will cover 50 square feet and cost $18.00
the pool will be filled when water is leveled 6" from the top of pool
there are approximately 7.48 gallons of water per cubic foot
Rectangle shape pool 36.0 long and 20.0 wide from top Answered by Stephen La Rocque. 





The volume of a hopper 
20070323 

From amitesh: Let me know how to calculate the tonnage of hopper / bins / chutes of different sizes and dimensions. Answered by Penny Nom. 





How many yards of soil is 55 quarts? 
20070320 

From Claudette: Costco sells bags of dirt in the quantity "55 quarts".. This makes no sense to me.
How many yards of soil is 55 quarts?
Thanks! Answered by Stephen La Rocque. 





How many hours will it take to fill completely? 
20070319 

From Leslie: If a rectangular prism measures 8" and measures 12" by 16", what is it's volume? If after 8 hours the prism is 6" full, how long will it take to fill and how many hours will it take to fill completely? Answered by Stephen La Rocque. 





The volume of a tube 
20070317 

From Tiffany: If I have a 42" diameter tube with 3 1/2" walls and 108" in length. How may gallons of water will it hold?
Thank you,
Tiffany Answered by Penny Nom. 





A water treatment plant 
20070317 

From Elvia: A water treatment plant is built with three cylindrical tanks to contain the water for a town. Each tank has a radius of 15 feet and a depth of 25 feet. If there are 7.5 gallons in a cubic foot of water, approximately how many gallons of water can be treated at the plant at any one time? Answered by Penny Nom. 





A steel pipe pile 
20070308 

From Sean: Need to fill a 18" OD x 60 feet steel pipe pile with a wall thickness of 1/2" What is the amount of concrete I need in order to fill? Thank you Answered by Stephen La Rocque. 





An excavation 
20070307 

From Brandon: you have and excavation area 140' long by 20' wide by 3' deep. What is the excavated volume? Answered by Penny Nom and Brennan Yaremko. 





How much soil do I get? 
20070307 

From Robbi: I have a garden area that is 19 feet by 11 feet and I would like it to be 2 feet deep. I need to know how much soil to get in feet and yards. Could you please give me the formulas to figure this out. Thanks Robbi Answered by Penny Nom and Melanie Tyrer. 





How much fill I would need 
20070306 

From Tracey: Oh am I confused! I need to know how much fill I would need to cover an area that is 28 feet in diameter by 8 inches deep. Thank you ... Answered by Penny Nom. 





One acre of water, one foot deep 
20070305 

From Jeff: If you have one square acre of ground flooded with one foot of water and a pump that pumps 1000 gallons a minute how long would it take to drain the one acre of ground? Answered by Penny Nom. 





The volume of a trailer 
20070304 

From Ron: I just can not seem to work this out, i think it is old age catching up with me, I am buying a trailer that is 25 feet long 7.5 foot wide and with 4 foot sides and i am trying to work out how many m3 it will hold can anyone help. Thank you in advance for any help. Regards Ron Answered by Penny Nom. 





A cylinder with a hemispheric cap 
20070225 

From lee: i have a diagram of cylinder with a height of 1.260m and radius 0.340m a hemisphere of radius0.400m is bonded to one end of the cylinder with a constant overlap of 0.06m between them a cylinder of radius 0.170m and length 1.280m is bored out of the composite body what is the volume remaining
also the composite body is to be painted i need to calculate the total area to be covered
could you please have a look thank you Answered by Penny Nom. 





The volume of a cone 
20070224 

From SAFDAR: How to derive the formula for volume of cone? Answered by Penny Nom. 





A concrete slab in the shape of a regular hexagon 
20070219 

From Mandy: Hi, We are laying a concrete slab in the shape of a regular hexagon with each side being 2m long. The slab will be 10cm thick. How much concrete will we need? Thank you ever so much! Mandy Answered by Penny Nom. 





A concrete foundation 
20070215 

From Jeremy: BiltWEll Construction needs to create a concrete foundation. 5ft deep measuring 60ft by 32ft, outside dimensions, with walls 7in. How many cubic yards of concrete will they need? Answered by Penny Nom. 





The volume of a prism 
20070214 

From jasmine: What is the formula to find the volume of a triangular prism Answered by Penny Nom. 





Cubic inches 
20070213 

From Renee: a glass has a height of 3 inches and a radius of 2 inches. about how many cubic inches of fwater will the glass hold? and how do you figure the answer? thank you...................renee Answered by Gabriel Potter and Melanie Tyrer. 





Volume of an inner tube 
20070210 

From Bubba: For a science project, I'm collecting methane gas in an inner tube. In addition to measuring psi of the inner tube, I'd like to calculate the volume of gas collected. What is the formula for or how would I calculate the volume of an inner tube? I appreciate any help you can give me.
Thanks so much. Bubba Answered by Penny Nom. 





The capacity of a tank 
20070208 

From lorn: what is the capacity of a tank height is 110 feet diameter is 24 feet Answered by Brennan Yaremko. 





Yardage of dirt fill 
20070202 

From Gene: I am removing dirt then replacing it with good dirt. I need to know how many yards of fill dirt it would take to fill a diameter 165 feet with fill of 13 ft would take how many cubic yards of dirt. Answered by Penny Nom. 





Price of topsoil 
20070202 

From Tyler: I need to convert cubic yards to square feet. I have topsoil that is $34.30 a cubic yard and I need to know what the price is in square feet. The depth is 18". Answered by Penny Nom. 





The volume of a cone 
20070131 

From ajay: WHY VOLUME OF CONE IS ONE THIRD OF THE VOLUME OF CYLINDER? Answered by Penny Nom. 





The density of an irregular wooden block 
20070130 

From Carlos: I'm trying to help my son but I don't really have too much knowledge about this topic. he is been asked to convert 10 milliliter to gram, I think that since 1 g = 1ml the answer will be 10 g also there is another question of how of the density of an irregular wooden block is affected if: a) the center is hollow: b) the block is not completely submerged when determining the volume. Answered by Stephen La Rocque and Penny Nom. 





Concrete paving blocks 
20070129 

From Engelbert: Readmixed concrete is sold by the cubic yard. A landscape contractor wants to form concrete paving blocks that are rectangular solids with dimensions 36 inches by 36 inches by 6 inches. Assuming there is no waste, how many such blocks can she expect to make from one cubic yard of concrete? (1 yard= 36 inches) Answered by Stephen La Rocque. 





Concrete slab 
20070126 

From Cindy: How much concrete will it take to pour a slab 16ft.By 18ft. 3inches deep Answered by Penny Nom. 





The volume of a pool 
20070123 

From Steve: how do we measure the cubic feet of a pool. The pool is 50 feet long by 40 feet wide by 4 feet at the shallow end and 9 feet at the deep end. Answered by Penny Nom. 





Calculating a person's volume 
20070120 

From James: Hi i am currently trying to calculate my volume. I have tried to do this using a tank of water and measuring the difference. i worked out that my volume is 112 litres. my question is that i want to make a box that would hold my volume and so i need to convert it into centimeters. i know that there are 100 cm^2 in a litre. if i divide this by 4 i would be 91x91x91ft. is this simply to do with density. if so how could i make this more realistic? Answered by Stephen La Rocque. 





A formula for figuring a tanks volume at various levels 
20070120 

From Dave: I know there has to be a general formula to figure out a tanks volume where as you know the total volume but you need to know what it will hold at various levels measured in 1/8th inches in depth and that you may be able to plug this formula into a program like say excel and thus create a chart unique to that tank. But for the lack of me I can not figure it out. Answered by Stephen La Rocque. 





Depth and volume in a cylindrical tank 
20070120 

From Andy: I need to fill a 10 foot diameter by 35 foot long cylinder 85% full. Is there a way to calculate at what depth equals 85%? ie, if I put a stick in the tank would it be at 8.5 feet? Answered by Stephen La Rocque. 





I need to store 26600 gallons of water 
20070117 

From Mauricio: I have to figure out the "height" of a square tank that is 18' wide and 18' deep, so I can store 26600 gallons of water? Answered by Stephen La Rocque and Penny Nom. 





The volume of a frustum of a pyramid 
20070117 

From Sam: Find the volume of a frustum of a pyramid with square base of side b, square top of side a, and height h. Answered by Penny Nom. 





The volume of a sphere 
20070116 

From Anshul: How to prove or find the volume of sphere? Answered by Harley Weston. 





The volume of a box in cubic yards 
20070111 

From Robert: i have a box 44inch high 16foot long on top and 8 foot long on the bottom 5foot wide how do i find the cubic yards Answered by Penny Nom. 





Calculating rainwater volume 
20061230 

From Mark: Trying to calculate 1" rainfall on a 1000 sq' roof=how many gallons of water would collect in our cistern. Answered by Stephen La Rocque. 





How many gallons of water does an 8 inch pipe that is 50 foot long hold? 
20061229 

From Bryan: How many gallons of water does an 8 inch pipe that is 50 foot long hold? Answered by Penny Nom. 





Drilling holes in a cube 
20061212 

From Liz: What is the volume of the solid remaining if a unit cube has a hole drilled thru one face to the opposite side and the hole that is drilled is a cylinder of unit diameter. Then the cube is rotated and an identical hole is drilled from an untouched face to the opposite side. Then the cube is rotated and an identical hole is drilled between the last two untouched faces. This will result in the cube vertices and the remaining volume of the cube falling into 8 parts. What is the total volume of these 8 parts. How is this volume calculated? Answered by Penny Nom. 





The volume of an irregular tetrahedron 
20061206 

From Hai Van: Could you please show me the way to calculate the volume of an irregular tetrahedron Answered by Penny Nom. 





Building a corral 
20061122 

From Dennis: I'm building a corral and need to know how many holes 6"x24'' in a yard of concrete Answered by Stephen La Rocque and Penny Nom. 





The volume of a box 
20061116 

From Sam: I have this box to mail and i would like to find out the cubic foot of the box.The W52 D13 H 37 inch cubic Answered by Penny Nom. 





A container to hold 600 gallons of water 
20061107 

From Cissy: What size rectangular tank would I need to hold about 500600 gallons of water. Answered by Penny Nom. 





3.253 cubic meters of water 
20061031 

From Elaine: a tank full of water that has a volume of 3.253 cubic meters would have a mass of? Answered by Penny Nom. 





Concrete tubes 
20061023 

From Rick: I have 36 18” concrete tubes to fill with 36” of concrete. How much concrete will it take to do this job Answered by Stephen La Rocque. 





How many 1 square 3/8 thick pieces of steel can you get from one cubic foot of steel? 
20061012 

From Jana: How many 1 square 3/8 thick pieces of steel can you get from one cubic foot of steel? Answered by Stephen La Rocque. 





I have a 3000 sq ft house ... 
20061010 

From Ann: I have a 3000 sq ft house and need to use flea foggers. Each fogger treats 6000 cubic feet. How many do I need? Answered by Stephen La Rocque. 





The volume of a hexahedron. 
20061004 

From A student: How do i compute volume of a generic hexahedron with all its faces being quadrilateral? Answered by Penny Nom. 





Filling a swimming pool 
20061004 

From Jon: what would be the formula to fill a swimming pool in with dirt that is 15ft wide,36ft long and is 8ft deep to 3ft deep Answered by Penny Nom. 





A concrete foundation 
20061002 

From A homeowner: I am pouring a concrete foundation 8" X 14" X 23'. How many cubic feet of concrete do I need? Answered by Penny Nom. 





The volume of a cube 
20060929 

From Greg: Nicolai said that 6 billion can represent the volume of a cube. How many units long is the cube? How do you know?" Answered by Stephen La Rocque. 





A volume 
20060927 

From jc: If I have to pay storage charges on 45 cu ft. What size is that area L X W X H Answered by Stephen La Rocque. 





We need to know how many cubic yards of concrete to order for the job. 
20060925 

From Linda: We are pouring an additional drive way and shop in our back yard. The total square foot of all the concrete is 1200 and the concrete will be 3" deep. We need to know how many cubic yards of concrete to order for the job. Answered by Penny Nom. 





Cubic yards of sand 
20060920 

From Michael: How many compacted cubic yards of sand are there in 40 acres of land at a depth of 20 feet? Answered by Stephen La Rocque. 





How much water it will hold? 
20060920 

From Doug: I have thirty feet of piping that is two inches in diameter and I want to know how much water it will hold and the equation for solving the answer. Answered by Stephen La Rocque. 





A rectangular tank 
20060919 

From Milton: What size rectangular tank will I need to hold 841.5 gallons of water. The water level is 3'0" from the bottom of tank. Answered by Penny Nom. 





The volume of a triangular box 
20060912 

From Irene: How do I find the volume of a triangular box? Answered by Penny Nom. 





How much cement would I need? 
20060907 

From Lou: At a five to one mix how much sand/gravel and how much cement would I need for a 71/2 yard pour?
What formula would I use for this calculation. My sand/gravel is in a cone shaped pile and I know how to calculate that. I need to know if I have enough and how many bags of cement I need to buy. I will be using a engine operated cement mixer Answered by Harley Weston. 





Cubic feet 
20060906 

From Tom: How do I calculate cubic feet ? What is the formula? Answered by Penny Nom. 





I am pouring cement 
20060822 

From David:
I AM POURING CEMENT
8FT. X 8 FT. X 4 INCHES
8FT. X 8FT. X 5 INCHES.
8FT. X 8FT. X 5 1/2 INCHES.
WHAT IS THE FORMULA?
Answered by Penny Nom. 





How many cubic yards of soil is needed 
20060816 

From John: how many cubic yards of soil is needed to cover 750 square feet at a height of 3 inches? Answered by Penny Nom. 





A concrete semicircle 
20060815 

From John: I have to figure out how many yards of concrete I need for a semicircle. I have a radius of 21 feet and the concrete is 4" thick. I took 3.14 x (21)^2 then divided by 40 to get how many yards of concrete but that doesn't seem right. Answered by Penny Nom. 





Gallons of water in a well 
20060731 

From Martha: I have a shallow water well that is 30 feet in depth.
I have 8 feet of water in the well.
The water well is a 30 inch in diameter.
My question : How many gallons of water is in my tank? Answered by Penny Nom. 





The capacity of our hexagon fish tank 
20060726 

From Doug and Andrea: My name is Andrea and my son, Doug, and I were wondering what the capacity of our hexagon fish tank was but it’s been so long since I’ve been to school that I’ve forgotten the formula to do so. Would you please help us? The dimensions are: 27 ¾ W x 24L x 29H or one side (glass panel) is 14W x 29H. Answered by Penny Nom. 





How many bags of concrete will we need to use? 
20060720 

From Sue: We are trying to pour some concrete
The area measures 26 ft long x 20 in wide. We want to pour the concrete 3 in thick.
One bag covers .41 cu. ft.
How many bags of concrete will we need to use? Answered by Penny Nom. 





Volume of rainfall 
20060718 

From Randy: Calculate the amount (in gallons)of rainfall .98 inches will put over an area of 3.76 acres. Answered by Stephen La Rocque. 





Ounces of water to grams 
20060716 

From Liza: How many grams is in 10 ounces? I'm asking this question because i just bought a sea monkey and it says add 10 ounces of water and I don't know what that means. I have asked my parents but neither of them know. Answered by Stephen La Rocque. 





Concrete for a chicken coop floor 
20060713 

From Chelsea: How much concrete for a chicken coop floor? The dimentions are 3 slabs, 30 feet long and 4 inches thick, 6 feet 6 inches wide. One slab is 41 feet long, 6 feet 6 inches wide, and 4 inches thick. Answered by Stephen La Rocque. 





Some plumbing calculations 
20060702 

From Steve:
I am preparing to write my journeyman plumber ticket and would appreciate answer/solutions to the following math questions along with the formula to solve them
 A range boiler is 16 in. in diameter and 4 ft high. How many gallons will it hold ?
 What would the weight in Kg be if the pipe was .4 of a meter in diameter and it was 8.6 m in length
 An oil storage tank is 4 m in diameter and 6 m high. How , many liters of oil can be stored
I thank you in advance for your help ... all math books I have are US and nothing is Metric
Answered by Stephen La Rocque and Penny Nom. 





Order of operations 
20060629 

From Jaden:
(1) A triangle has vertices at (3,3) (7,3) and (2,5). What is the area of the triangle?
Is there a way of doing this so that you dont have to graph it? If the x axis is horizontal can i say it is the base and the yaxis is horizontal meaning the height. Would I be able to do this...3 to 7>9 spaces, 3 to 5>7 spaces9(7)63/2=31.5
(2) A cube has a surface area of 54 square centimeters. What is the volume of the cube in cubic centimeters?
Answered by Stephen La Rocque. 





The volume of a building 
20060628 

From A student: a building is 8 feet wide and 16 feet long. it has a flat roof that is 12 feet high at one corner, and 10 feet high at each of the adjacent corners. what is the volume of the building? Answered by Penny Nom. 





I have a ditch how many tons of dirt will it take 
20060625 

From Scott: I have a ditch 200 feet long 10 feet wide and 5 feet deep.How many tons of dirt will it take to fill it? Answered by Stephen La Rocque. 





Gallons in a pool 
20060621 

From Dave: is it possible to find out how many gallons of water is in my 18 foot x 12 foot pool it is also about 4 and 1/2 feet deep? Answered by Penny Nom. 





How many bags will it take to cover the area? 
20060614 

From Ken: I have area of 160 sq ft. I want to put mulch in the area 2 inches thick. The bag of mulch comes with 2 cu ft of mulch per bag. How many bags will it take to cover the area? Answered by Penny Nom. 





A 52 cubic foot box 
20060614 

From Konstanze: I need to figure out what LXHXW I need to create a 1.5 cubic meter or 52 cubic foot volumethere is an answer in your database that relates to this..but it does not give the formula to go from cubic feet/inches to a measurement for a box.
Empirically I can figure out that 3 x 3 x 3 equals 27 and that 3.5 feet (42") x 3.5 x 3.5 equals 42.87 and 3.75 x 3.75 x 3.75 equals 52.73 which is about 1.5 cubic meters (1cubic meter = 52.971643 cubic feet) i.e a box 45 x 45x 45 "
There must be an easier way. Answered by Penny Nom. 





The volume of a roll 
20060609 

From Yogesh: I have a roll which height is 63 inches & width is 11 inches i want to know that how to calculate the cubic meter of this roll Answered by Penny Nom. 





A volume of revolution 
20060607 

From Colleen: Find the exact volume in cubic units generated by rotating a region, R, around the
yaxis, given that R is the region bounded by the curve y = x^{3} and the lines x = 1 and
y = 8. Answered by Penny Nom. 





Putting in a sidewalk 
20060531 

From Sandra: I am putting in a sidewalk the measurements are 12 feet by22 inches ,by 4inchs how many bags of cement will I need? Answered by Penny Nom. 





what is the cubic feet of 18... 
20060527 

From A student: what is the cubic feet of 18"x18"x24"? Answered by Penny Nom. 





Cubic yards of sand 
20060526 

From Steve: I need to cover an area with sand that is 30 feet wide and 60 feet long and I need the depth of the sand to be 1/4 inch thick. How many cubic yards of sand will I need? Answered by Penny Nom. 





differentiate the volume of a cylinder with V respect to h 
20060524 

From A student: differentiate the volume of a cylinder with V respect to h Answered by Stephen La Rocque. 





The volume of a cylinder 
20060522 

From A student: Show that a volume of a cylinder equals to v = A^{2} / (4πh)
where h= height of the cylinder
A = area of a original paper Answered by Penny Nom. 





A concrete driveway 
20060521 

From Diane: I am trying to estimate how many cubic yards of concrete I will need to pave my driveway. I have an area that is 30 ft wide by 25 ft long and then goes into an area that is 10 ft wide by 219 foot long. I would like to make this 4 inches thick. How many cubic yards of concrete will it take to do this? Answered by Penny Nom. 





A box with an interior of 1.26 cu. feet 
20060519 

From Maria: I am trying to build a box with an interior of 1.26 cu. feet with all sides equal. Answered by Stephen La Rocque and Penny Nom. 





What is the radius of the sphere? 
20060517 

From Jimmy: The surface area and volume of a sphere are both equal to the product of 4digit whole numbers and pi. What is the radius of the sphere? Answered by Stephen La Rocque. 





The volume of water in a sphere shaped water tower 
20060514 

From Dan: I work in the water industry, providing automatic controls for water systems. I was wondering if there was a formula for calculating the volume of water in a sphere shaped water tower? With the use of a pressure gauge we know the elevation of zero water {the bottom of sphere) and the overflow elev. (near the top of sphere) I would like to calculate how many gallons are at any elevation in between. Answered by Stephen La Rocque. 





Landscaping 
20060511 

From Luke: HOW MANY CUBIC YARDS OF CONCRETE WILL IT TAKE TO FILL UP A BOX 20FT.X20FT.X6IN DEEP?
HOW MANY CUBIC YARDS OF CONCRETE WILL IT TAKE; I HAVE A 12FT.IN DIAMETER POND AND I WANT TO PUT A 3FT.SIDEWALK AROUND THE OUTSIDE OF IT? Answered by Stephen La Rocque. 





A box with volume 0.78 cu ft 
20060510 

From Sherrina: i need to build a box that equals .78 cu ft any ideas on how i do this Answered by Penny Nom. 





How much does 1300cc of liquid weigh? 
20060428 

From Debra: How much does 1300cc of liquid weigh, and how is the formula equated? Answered by Stephen La Rocque. 





How many gallons in a cubic foot? 
20060424 

From Jana: How many gallons in a cubic foot? Answered by Stephen La Rocque. 





Volume of a tennis ball can 
20060416 

From Jon: Tennis balls are generally packaged in circular cylinders that hold 3 balls each. The diameter of a tennis ball is 6.5 cm. Find the volume of a can of tennis balls. Answered by Stephen La Rocque. 





A 20 foot container 
20060405 

From Karen: can you tell me how many cubic square meters are in a 20 foot container Answered by Stephen La Rocque. 





The Mitchell Park Domes 
20060401 

From Nicole: I would like to know how I could find the volume underneath the Mitchell Park Domes? The Diameter of the Domes is 140ft, 85ft high and 15,000 square feet. Answered by Stephen La Rocque. 





The volume of water in a cone 
20060321 

From Ghulam: A vessel has the shape of an inverted cone.The radius of the top is 8 cm and the height is 20 cm. Water is poured in to a height of x cm.Show that if the volume of the water is V cubic cm,then V=(4/75)pi x3. Answered by Penny Nom. 





Quarts, liters cubic yards and soil 
20060319 

From Kathy: I am trying to find out how many quarts of dirt there are in a yard of dirt. The local flower store sells bags of dirt that are 20 quarts or 22 liters for $1.25 and another store sells a yard of dirt for $25.00. Which is the better deal? Answered by Penny Nom. 





Building a flower bed 
20060317 

From Bobby: I am building a flower bed 60 ft long by 8 ft wide by 3 ft deep. How much dirt will it take to fill it with top soil/dirt. Answered by Penny Nom. 





What is the height of the pot? 
20060310 

From Michelle: If a pot is 11 inches in diameter and holds 5.8 litres what is the height of the pot?  assuming it is a cylinder. Answered by Stephen La Rocque. 





The number of gallons in a tank 
20060309 

From Doug: We have a round tank that is 216 inches long 64 inches wide across ; how do we find the number of gallons it could hold ? Answered by Stephen La Rocque. 





Balls in a cylinder 
20060303 

From Roxanne: If a cylindrical can holds three balls with no room to spare, explain how to find the volume of the air that surrounds the balls in the can. Yet the balls have a diameter of six inches Answered by Stephen La Rocque. 





Volume 
20060302 

From Irene: how do you find the volume in cubic units. i need the basic formula to help my child. Answered by Penny Nom. 





A cone with an oval as base 
20060301 

From Richard: I am trying to find the volume of a cone that is not round but oval. Answered by Penn Nom. 





The volume & surface area of a rectangular pyramid. 
20060227 

From Cheryl: My daughter is working on a math project & we are having a hard time finding the volume & surface area of a rectangular pyramid. Can you help us with this? Answered by Penny Nom. 





One acre 20 feet deep 
20060216 

From Bob: How many cubic yards of material are in one acre of land approximately 20 feet deep? What is the approximate weight of one cubic yard of Black dirt, Gravel, and Sand? Answered by Penny Nom. 





A concrete slab 
20060213 

From Cheryl: A concrete area that will be used for picnic benches will measure 20 ft on each side. The concrete slab will be 8 inches deep. How many cubic feet of concrete will be needed to construct the patio? Answered by Penny Nom. 





Concrete in a foundation 
20060208 

From Philippe: Can you please help me determine how many cubic yard of concrete I need to purchase for a foundation that is 50' by 25.5 by 8' height and how many cubic yard would I need for the slab that is 50' by 25.5 by 0.5 Answered by Penny Nom. 





Why 1/3 in the volume formula for a pyramid? 
20060203 

From Becky: why is the formula for finding the volume of a pyramid divide by 3? Answered by Penny Nom. 





The box of maximum volume 
20060201 

From Elizabeth: A box factory has a large stack of unused rectangular cardboard sheets with the dimensions of 26 cm length and 20 cm width.
The question was to figure what size squares to remove from each corner to create the box with the largest volume.
I began by using a piece of graph paper and taking squares out. I knew that the formula L X W X H would give me volume. After trial and error of trying different sizes I found that a 4cm X 4cm square was the largest amount you can take out to get the largest volume. My question for you is two parts
First: Why does L X H X W work? And second, is their a formula that one could use, knowing the length and width of a piece of any material to find out what the largest possible volume it can hold is without just trying a bunch of different numbers until you get it. If there is, can you explain how and why it works. Answered by Penny Nom. 





Cubic yards of dirt 
20060128 

From Greg: How many yards of dirt do i need to cover an area of 1000 ft long, 20 ft wide and 3 inches deep Answered by Penny Nom. 





Concrete tubes 
20060114 

From Paul: I have 15 tubes. Each tube measures 12in.x 48in. I have to fill each one with concrete. How do I figure how many cubic yards of concrete I will need? Answered by Penny Nom. 





The volume of a piece of furnature 
20060110 

From Kimberly: What is the cubic feet for a piece of furniture that is 38" wide X 45" tall X 18" deep Answered by Penny Nom. 





Barrels of oil in a tank 
20060109 

From Francis: How many barrels of oil (42 gallons of oil in one oil tank) would there be in an oil tank that was 15 feet tall and 10 feet across? Answered by Penny Nom. 





The volume of a cylinder 
20060104 

From Doug: I have a Cylinder which is 34" x 72" how many gallons will it hold? Answered by Penny Nom. 





Cubic yards of fill 
20051223 

From Mike: And I have a question in regards to the amount of fill needed to bring a vacant lot up to "grade level".
The lot is 112' x 87' and I need to bring in fill to elevate the finished level up 4'. Answered by Penny Nom. 





A concrete patio 
20051206 

From Anne: If you are making a concrete patio 4 inches thick, what is the area of the largest patio you could make if you ordered 2 cubic yards of concrete? Answered by Penny Nom. 





Cubic yards of concrete 
20051106 

From Cyndi: I have a carport that is 20' x 31' and a driveway that is 12' x 18' that requires a 3" depth of concrete.
I need to now how many cubic yard it will need to complete these two areas. Answered by Penny. 





Volumes 
20051031 

From Diane: My name is Diane and I am a returning student to a vocational technical school.
As a reference point to see what I did/didn't remember from my HS math days, I was sent home with a 75 problem math packet. I was fine until I got to computing:
1. the volume of a cylinderis it pi r^{2} h?
2. the volume of a cone is it pi/3 r^{2} h?
3. the volume of a sphere I can't even hazard a guess.
Help my last classroom was 23 years ago, and I've forgotten far too much! Answered by Penny Nom. 





A two cubic foot box 
20051027 

From Michael: I need to make a box that measures two cubic feet. It will be used to items in to determine if an inmate has to much property. They can only possess 2 cubic feet of property. How can I convert that into measurements in inches for feet so I can make a box with a lid that is 2 cubic foot. I sure hope you can help me Answered by Penny Nom. 





How many gallons will it hold? 
20051016 

From Scott: I am building a pond and need to convert the cubic dimensions into gallons in order to know what size fountain pump to purchase.
My pond is 1 foot deep x eight feet long x three feet wide.
How many gallons will it hold? Answered by Penny Nom. 





Volume of a tank 
20050911 

From Jim: We own an Rv and need to actually know the volume of our fresh water tank. I think I'm getting the run around from the manufacturer. I'm unable to locate my chemistry books from from collage. I know there is a formula for the volume of a rectangle some place. Answered by Penny Nom. 





The volume of the earth in gallons 
20050818 

From Daniel: I would like to know how to find the volume of the Earth in gallons. Answered by Penny Nom. 





The volume of soil needed to fill a planter 
20050810 

From Phil: I need to calculate the volume of soil needed to fill a planter box that measures  880mm W x 6080mm L x 900mm D. Answered by Penny Nom. 





Cubic feet 
20050810 

From Selene: This is my math question I need to convert these inches to cubic feet
34"W x 34"H x 34"L Answered by Penny Nom. 





Cubic yards of sand 
20050804 

From Beth: I am trying to figure out how much sand I will need for ground cover under my children's playset. The area to cover is 30' x 30' and I want 4 inches of sand. Answered by Penny Nom. 





Cubic feet in a mobile home 
20050722 

From Jeanne: my mobile home is 24 x 56. I'm trying to find out how many cubic feet this is. I'm going to set of some bug bombs and it says 1 can will cover 4000 cubic feet. I don't know how to figure my cubic feet. the ceilings are 8 ft high everywhere but the living and dining room. They are vaulted and approximately 10 feet at the peak. I just need an estimate. Answered by Penny Nom. 





A melting ice sphere 
20050709 

From A student: A 2 meter diameter sphere of ice melts at 1.5 millimeters per minute. How many minutes will it take to fill up a hexagonal container measuring 1.5 meters on a side, and 0.8 meters deep? Answered by Penny Nom. 





The volume of a pool 
20050709 

From Douglas: I have a pond that I need to treat with an anti algae solution which needs to applied based on the volume of water in the pond (in gallons).
The rough diameter of the surface of the pond = 25 ft
The depth of the pond = 8 ft
The pond shape is conical
How many gallons of water are in my pond? Answered by Penny Nom. 





Digging a hole for a pool 
20050608 

From Debra: I need to have dirt hauled away from my built in pool and the haulers are asking me how many yards of dirt there is. How would I figure that out? It is a 24 ft round pool and 3 inches of soil depth was dug out. Answered by Penny. 





The volume of a sphere. Why 4/3? 
20050530 

From Lauren: You know when you find the volume of sphere? I know the formula is V= 4/3 pi r^{3} but why do they use 4/3? Answered by Penny Nom. 





Square feet and cubic feet 
20050530 

From Kim: Is there a relationship between square feet and cubic feet? Answered by Penny Nom. 





The volume of a hopper 
20050528 

From Brian: I would like to know the volume of this rectangular hopper. can you help Answered by Penny Nom. 





Volume and surface area of a prism 
20050429 

From Melissa: Can you please tell me if the volume and surface area of a prism can ever be the same? Could you please explain why or why not. Answered by Walter Whiteley. 





How much sand is in a pile? 
20050416 

From Larry: I was wondering if there is a formula for determining how much sand would be in a pile. I am a student in medical school, and this is a bonus question for a test. I hope you can help me. Answered by Harley Weston. 





Some liquid in a cone 
20050403 

From Vasuki: There are 2 right cones, height is X. one of them is filled from the bottom up (round side) = x/2, when you invert the cone and add the same amount of liquid inside the second cone, what is the HEIGHT of the liquid? Answered by Penny Nom. 





Gallons in a tank 
20050402 

From Jim: Would you be so kind as to help me with a problem? My memory has failed me in remembering how to calculate how much liquid in gallons a tank will hold. The tank is 8 feet long and 44 inches in diameter. Answered by Penny Nom. 





Gasoline in a cylindrical tank 
20050323 

From Jennifer:
Gasoline is stored in a tank which is a cylinder on its side. Height of fuel is "h" meters and the diameter is "d". The length is "l".
I need to find the amount of gas in the tank when the height is h and also to calculate the fraction of how full it is.
Also, the part I am really confused on is this one,
E(h/d) is the error of the function of h/d, when h/d is used to measure how full the tank is. For what value of h/d is the error maximal?
Answered by Penny Nom. 





The volume of a stock tank 
20050313 

From Cord: I am a farmer and I have recently installed a new stock tank which is 1650" in circumference and 10' deep. How many gallons of water will it hold? Answered by Penny Nom. 





I need to fill an area with rock 
20050304 

From Kelly: if I need to fill an area with rock that is 64 feet long by 4 feet wide and 1 foot 2 inches in depth
how many tons of rock will this job require?
it is also sold by cubic yard how many of these cubic yards will I need? Answered by Penny Nom. 





The volume of a sphere 
20050225 

From Stephanie: find the volume of a sphere that has a diameter of 12 cm.
please show me how to work this problem Answered by Penny Nom. 





The capacity of a dryer 
20050223 

From Darlene: I am trying to figure out the capacity of my dryer. I need to know the size in order to buy a new one. The drum within measures 27" in diameter and 18" deep. I know that I am looking for an answer in cubic feet but am not sure how to determine this.
Answered by Penny Nom. 





The weight of some concrete 
20050215 

From Jordan: I have 6 acres of concrete that is 3 feet thick the aprox. weight of 1 cubic yard of concrete is 4024 pounds I am trying to find out how much my 6 acres weighs. fortunately my concrete is 3 feet deep. Answered by Penny Nom. 





The volume of an aquarium 
20050201 

From Selena: Im trying to figure out the amount of gallons from a rectangle 48x20x12? Answered by Penny Nom. 





The side of a cube 
20050117 

From Jake: I have one for you that's got me stumped. Is it possible to calculate the dimensions of a square if I have the cubic feet? Say I know the package to be 180 cubic feet. Answered by Penny Nom. 





Gallons in a cylinder 
20041229 

From Dean: I have 2 cylinders:
Cylinder A = 8'D x 12'H
Cylinder B = 10'D x 15'H
Each 1ft represents how many gallons of fluid?
Cylinder A=?
Cylinder B=? Answered by Penny Nom. 





The volume of a sphere 
20041130 

From Lyndsay: twenty cubic metres of air are pumped into a spherical hot air balloon with each given diameter: 1.0m; 2.0m; 3.0m; 4.0m; 5.0m;6.0m
a)calculate the new diameter, new suface area, and new volume of each balloon. Answered by Penny Nom. 





Volume of a box 
20041118 

From Catherine: I need to find a formula to calculate the amount of liquid would hold. maybe the volume or something. its a square box used to hold liquid on a farm . we want to measure how much liquid it can hold. Answered by Penny Nom. 





Cubic yards of concrete 
20040929 

From Tanya: We are starting up a new business and for the business we will be required to order concrete for various shapes. Right now we have a job that requires a concrete slab that a decagon it is 1403/4" from flat side to flat side, 74" from point to center and each flat side is 46" The pad should be 4" thick with 12"x12" continuous footing. Answered by Harley Weston. 





The volume of a pile of mulch 
20040922 

From Sam: Is there a formula to determine the cubic feet of something in a pile. IE I need to determine the cubic feet of a pile of mulch. The pile comes to a peak, so the length and width decrease as the pile increases. Answered by Penny Nom. 





Volume 
20040916 

From Jonathan: I have an area of 22ft x 43 ft, 6 inches high
Sq. ft..946
sq. yds...105.1
What is the cubic feet and cubic yards for this dimension. Answered by Penny Nom. 





A copper sphere 
20040912 

From Irfan: The radius of a copper sphere is 3cm. If a wire of 0.4 diameter is drawn by melting it,what is the length of this wire? Answered by Penny Nom. 





Cubic yards 
20040901 

From Garnet: I have the dimensions of 16 feet by 10 ft and 3 1/2 inches deep how much concrete do I need. Answered by Penny Nom. 





15 cubic yards of dirt 
20040822 

From Barry: My question...what is the equivalent of 15 cubic yards of dirt? Answered by Penny Nom. 





Cubic yards of dirt 
20040811 

From A parent: How many cubic yards of dirt would it take to fill an area that is 325 feet by 325 feet and is 3 feet deep? Answered by Penny Nom. 





Water in a cone 
20040728 

From A student: A vertically inverted cone( i.e. vertex down) has a radius 7
inches and height 24 inches. Water is filled to one third of its
height .Find the ht of water when cone is turned upside down Answered by Penny Nom. 





How much loam to fill a hole? 
20040619 

From Harry: Can you tell me how much loam I would need to fill a hole 15 feet in dia. x 6 inches deep. Answered by Penny Nom. 





A garden space 
20040616 

From Carol: We have a 17' x 19' garden space. If we want it a foot high raised bed, how many cubic yards of topsoil do we need? Answered by Penny Nom. 





Cubic yards in a pool 
20040530 

From Jerry: HAVE A AREA WHERE I HAD A 18 FOOT ROUND POOL.
THE DEEPEST PART IT WAS IN THE GROUND WAS AROUND 7 INCHES TAPERING DOWN TO AROUND 4 TO FIVE INCHES AND A LITTLE OF THE ONE SIDE ALMOST AT GROUND LEVEL...HOW MANY YARDS OF DIRT WOULD I NEED TO FILL IT IN???? IS THERE A FORMULA FOR THAT.......COULD YOU FIGURE THAT FOR ME?
Answered by Penny Mon. 





Programming without trig functions 
20040525 

From Derek: I am a programmer trying to calculate the following.
What is the formula to find the crosssectional area of a cylinder with out using any trig functions? or better yet, how can you calculate any given volume in a cylindrical tank with spherical heads with out trig functions?
I am using a PLC (programmable logic controller) to do this and trig functions are not available. Answered by Harley Weston. 





Volume of a box 
20040523 

From A student: The area of the top of a closed rectangular box is 252cm2, the area of the front of the box is 105cm2, and the surface of the box is 834in2 (or 5380.64cm2). What is the volume of the box? Answered by Penny Nom. 





Yards in a concrete driveway 
20040427 

From Bobbi: I am wondering how many yards of cement I need for a 49 by 45 area, 5 inches thick. I am a stay at home mom who is not very good at math and I want to pave my drive way. Also what would the yardage be for a 6 inch thick drive way with the same area. Answered by Penny Nom. 





Water in a pipe 
20040425 

From Marlean: How much water would be in a 480 foot one inch inside diameter pipe?? In imperial gallons please. thanking you in advance for your help in this matter.
Answered by Penny Nom. 





The volume of a sphere 
20040326 

From Mike: I was in class today and I learned how to calculate the volume of a sphere. I understood it easily but can't find the logic behind it. So here are my questions, in the formula why is the radius cubic and not squared? And what does 4/3 have to do with it? Answered by Penny Nom. 





Volume of a fuel tank 
20040301 

From Mike: I have a fuel ank for my big truck that has a radius of 24inches and a length of 65 inches. I am trying to compute the volume of fuel in the tank. I tried pie x the radius squared times the length but no usable results.
Can you help me please? Answered by Penny Nom. 





Gallons in a cylinder 
20040220 

From Jim: Please advise how to use the formula I saw for determining the number of gallons in a cylinder? This is how it was written
V = pi r2 h
. does this mean pie, or 3.14 X radius squared, X the height? If so please use a standard 55 gal barrel (1' R & 3' H) for example? Answered by Penny Nom. 





Areas, perimeters and derivatives 
20040215 

From Geoff: A recent lecture in my calculus class led me to realize that the derivative of the area of a circle, with respect to the radius is equal to the circumfrence. This also holds true for the relationship between the volume of a sphere and the surface area of that sphere:
why do these hold true? why is it only for circular objects? Answered by Harley Weston. 





The volume of a tetrahedron 
20040203 

From Joseph:
How do I calculate the volume of a bird tetrahedron. I'm trying to find out to get extra credit. I came with this idea while making a origami tetrahedron.
Joseph
P.S. Do you by any chance have instructions for orig ami figures. If you do, please send me some. Thanks!
Answered by Penny Nom. 





Volume of a tube 
20040114 

From Mike: where can you find how to get volume of a tube:
3 in across x 3 inch high
5 in across x 5 inch high
same formula for both. ONE will get the other. Answered by Penny Nom. 





A snowball melts 
20031211 

From Adam: A spherical snowball has diameter 10cm and density 0.75g/cm3. It is placed in a cylindrical can with diameer 12cm. After the snow melts it turns to water with density 1.0g/cm3. What will be the depth of the water in the can (to 1 decimal place)? Answered by Penny Nom. 





A fish tank 
20031126 

From Bill: How do I work out the volume and weight of water in a fish tank that is 36in x 14in x 12in? Answered by Penny Nom. 





The volume of an irregular tetrahedron 
20031124 

From Peter: How do I calculate the volume of an irregular shaped tetrahedron where: side a = 1.4 m side b = 1.4 m side c = 1.2 m and height = 0.75 m at the junction of sides a and b. Answered by Penny Nom. 





The volume of an earthen pit 
20030912 

From Bruce: This shape would occur at the four corners of a rectangular shaped earthen pit with sloping sides (1:1.5). Depth is 14'. Top dimensions are 170' by 158'. After calculating the easy volume components of this shape, we are left with the end corner pieces. 21' base, 14' height, side hypotenuse 25.24' and corner diagonal 32.83'. We're confused. Thank you for any help you may provide. Answered by Penny Nom. 





Water in a tank 
20030902 

From A parent: if a tank is 48 inches long 14 inches wide and 18 inches deep if a yardstick was inserted into the tank and measured 2 inches of water in the tank how many gallons of water would be in the tank. Answered by Penny Nom. 





How many cubic yards must I purchase? 
20030829 

From Walt:
I am trying to determine how much top soil I must purchase (by the yard). The area is 80' x 15' and I want it 3" thick. How many cubic yards must I purchase? Answered by Penny Nom. 





The volume of a fuel tank 
20030816 

From Phil: I hope you can help me out with a small problem. My boat has a fuel tank measuring 1680mm long x 630mm wide x 130mm high. Can you tell me how much fuel it will hold in both litres and imperial gallons. Answered by Penny Nom. 





Water in a cone 
20030812 

From Adrienne:
Water is poured into a tank in the shape of an inverted right circular cone.ð The height of the tank is 8 m and its radius at the top is 4 m. a. Draw and label a picture to represent this situation.ð (I know how to do this) b. Identify all variable quantities. (h = 8m, r = 4m) c. Find an equation that relates the variable quantities, and reduce the number of variable quantities to two. I was thinking about the equation V = 1/3 pi r^{2} h, which is the Volume of a cone, but I am stumped as to how I am supposed to "reduce the number of variable quantities to two." Can you point me in the right direction? Answered by Penny Nom. 





Yards and cubic feet 
20030811 

From Sonya: How many cubic feet are in a yard? Answered by Penny Nom. 





Liters in a pool 
20030805 

From A parent: I need to know how many litres in a 12 foot diameter, 3 foot deep pool? Any help much appreciated as I need to add the correct amount of chemicals Answered by Penny Nom. 





"cubic feet" of a refrigerator 
20030716 

From Ron:
Is the volume of a home appliance (e.g. fridge or freezer) calculated in a different way? I am planning to replace both my fridge and my freezer but I'm unable to determine what size replacement to get. For example, one company descibes their fridge as being 32"(L) x 30"(W) x 66" (H). I converted those measurements to feet (2.67 x 2.5 x 5.5) and I calculate the fridge to be 36.7 cubic feet. However, the company says the fridge is 18 cf. Answered by Chris Fisher. 





Volume of water in a pool 
20030706 

From An other: How many litres of water are in a pool that is 16 feet in diameter and 35 inches deep? Answered by Penny Nom. 





How much soil will be removed? 
20030702 

From Amy: My site is 1230' (eastwest) by 1300' (northsouth) and we need to remove 2 feet of soil from the entire site, how much soil will be removed? Answered by Penny Nom. 





The weight of a fish tank 
20030520 

From A ponderer: I had a question pertaining conversion units..I have a fish tank at home and the dimensions are 24, 44, and 48 inches, I want to find out how much it weighs in pounds when filled up with water...knowing water is 62.4 pounds per cubic feet...do I just divide the 62.4 pounds to 12 because I"m trying to find out through cubic inches. Answered by Penny Nom. 





The volume of air flowing in windpipes 
20030502 

From James: The volume of air flowing in windpipes is given by V=kpR^{4}, where k is a constant, p is the pressure difference at each end, R is the radius. The radius will decrease with increased pressure, according to the formula: R_{o}  R = cp, where R_{o} is the windpipe radius when p=0 & c is a positive constant. R is restricted such that: 0 < 0.5*R_{o} < R < R_{o}, find the factor by which the radius of the windpipe contracts to give maximum flow? Answered by Penny Nom. 





The surface area of a cube 
20030407 

From Sarah: if the volume of a cube is 64 cm, then what's the total surface area? I also want to know how to show my work. Answered by Penny Nom. 





Doubling the size of an object 
20030401 

From Dave: If I have a known surface area and volume of an unknown object and I want to double the size of the object, how do I find the new area and volume? Answered by Walter Whiteley. 





Filling in the back yard with dirt 
20030204 

From Joe:
We just bought a house and need to start filling in the back yard with dirt to level it out. I measure 37'x 56' by 2' deep on an angle. I will be building a retaining wall at the 2' deep portion. The slop will go from the 2' to nothing at the top or near the house. I can't remember how to get the Sq. foot or cubic yards. Answered by Penny Nom. 





Cubic yards in a gravel pile 
20030110 

From Ron: I am looking to find a way to measure gravel piles to get yards. They are generaly not square.it would be like pouring sand out of a bag into a pile. they generaly are concave in dimension. can you help. I have attached a picture to show a small scale what I am working on is in much larger volume. Answered by Harley Weston. 





A sphere with a hole  cylindrical shells 
20021211 

From Kathy: Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters.) You discover that both napkin rings have the same height, h.  Guess which ring has more wood in it and why.
 Check you guess: Use cylindrical shells to compute the volume of a napkin ring created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h.
Answered by Penny Nom. 





The dimensions of a box 
20021203 

From Paula: My son, who is in secondary school, needs to make a box with the inside dimensions of 1.25 cubic feet. It's supposed to be more in the shape of a rectangle than a square. I would like to know the equation to use to find the inside dimensions of a box if I know how many cubic feet (or inches) I need the inside to be. Answered by Penny Nom. 





The volume of a juice jug 
20021121 

From Edward: I try to find the measurement for a juice jug. I have the height of the jug and need the jug to hold 2.5 Liter of juice. Can you help me out with the formula. Answered by Penny Nom. 





The volume of water in a hose 
20021113 

From David: I trying to find out how much water 500 ft of 3/4 inch hose will hold. I'd also like to know how you figured the answer. Answered by Penny Nom. 





Sanding a wooden block 
20020907 

From Wanda: If a wooden block, 2in height, 3in width, and 6in length is sanded and 1/8 of an inch is removed from the top and from the bottom, how much is the volume of the block decreased? Answered by Penny Nom. 





Cubic yards of concrete 
20020824 

From Michael: if you have a 10" dia pipe 8' long how many cubic yards would it take to fill with concrete. how how would you go about figuring it out. and also if you would how many cubic feet, cubic inches in a cubic yard. i know you don't need to answer, seeing i am not in school, but would appreaciate it. Answered by Penny Nom. 





Gallons in a cylindrical tube 
20020821 

From Heidi: IF I HAVE A 12" DIA TUBE WITH 1/4" WALL AND 72" IN LENGTH HOW MANY GALLONS OF WATER WILL THIS HOLD Answered by Penny Nom. 





Volume of a sphere 
20020816 

From Rahul: How do i find the volume of a sphere without the knowledge of calculus? Answered by Walter Whiteley. 





A box that holds 22.4 liters 
20020707 

From Jon: How do I find the measurements required to make a box that holds 22.4 liters of something? Answered by Penny Nom. 





Cubic feet and cubic yards 
20020527 

From John: how do you find the cubic feet/cubic yard of area 10 feet wide by 15 ft long by 2 inches high Answered by Penny Nom. 





A 6,000 gallon tank 
20020428 

From Someone with a big tank: I was wondering if you can find out information about how much liquid fuel can fit in a 6,000 GAL. tank. Right now I do not have the exact dimensions of this tank but I will have it the 29th of April. Could you please Email me and let me know if you can answer this question after I have the correct specifications. Answered by Penny Nom. 





Cubic yards 
20020420 

From Pat: I HAVE AN AREA 10'x6'I WOULD LIKE TO PUT LOAM ON IT 5" DEEP HOW MANY CUBIC YARDS OF LOAM DO I NEED? Answered by Harley Weston. 





Catenary 
20020102 

From Jason: I am a high school math teacher. I was asked by a friend who is in architectural design for a method for determining the volume of what he called a Catenary. The Catenary curve is modeled by the equation y=a cosh(x/a). I ran into a mess when I tried to compute the volume of the solid formed by revolving that curve around the yaxis. Any help you can provide would be greatly appreciated. Answered by Harley Weston. 





A box of pants and shirts 
20011117 

From Debbie: I need to determine the volume of a box that is 4'HX4'WX4'L. The box contains uniform pants and uniform shirts. I need to know how many shirts and pants are in the box. When folded, the uniform shirt is .5 inches thick. The pants are also .5 inches thick. Answered by Penny Nom. 





The amount of gravel needed to fill a hole 
20011006 

From Rhett: My name is Rhett and my problem is...I am a contractor and I am having problems determining the amount of gravel(in tonnage) needed to fill this hole,the measurements are 60' in length,22' in width,and 14' in height....the problem is that it is not a usual box shaped hole or in this case a rectangle shaped hole,but more of a triangular shaped hole.I refer to the triangular shape as the interior shape of the crater not the exterior,which is shaped like the above dimensions.If you could help it would be greatly appreciated.P.s.This was a retaining wall project,built by myself, in front of a sloped end of a yard,so if you could imagine a 14" high hill with a landslide looking face,then build in your mind a three sided rectangle in front of it using the hill side that slopes as the fourth side of the rectangle,then you may be able to imagine what I mean as a triangular shaped interior of the hole. Answered by Penny Nom. 





A pile of sand 
20010514 

From Gul:
 Sand for use on icy roads is stored in a conical pile 14.2 m high and with a base diameter of 34.4 m
 calculate the volume of the pile
 if one sander can take 6.9 m of sand, how many sanders can be filled from the pile?
Answered by Penny Nom. 





Volume and surface area of a cylinder and a triangular prism 
20010331 

From Kevin: I was wondering how do you find the volume and surface area of a cylinder and a triangular prism. Answered by Penny Nom. 





A box with an interior of 1.25 cubic feet 
20010326 

From Gabe: I need a box with an interior of 1.25 cubic feet. I am using 3/4 inch material to make the box. What would the exterior dimensions be in inches? Answered by Harley Weston. 





Cubic feet 
20010220 

From Frances: I'm trying to calculate cubic feet from the dimensions of a machine given in inches. Width = 32" Height = 79.5" Length = 91.5" Weight = 3920 lbs Please help? Obviously I've been away from school too long!! Answered by Penny Nom. 





Building a circular silo 
20010124 

From Natasha: We wish to build a circular silo with internal diameter 10 feet. How much concrete will we need to pour the foundation, if we only need a 1 foot wide and 1 foot deep ring on which the silo walls will sit? Assume the 4 inch thick silo wall rests on the middle of the ring. Answered by Penny Nom. 





Square feet and cubic feet 
20010121 

From Jenny: How do I convert square feet to cubic feet? If I have 2000 square feet then how many cubic feet do I have? Answered by Harley Weston. 





Filling a tank 
20010102 

From Liting: Water flows into a rectangle tank which measures 4 m by 3 m by 2.8 m through a cylindrical pipe of radius 2.4 cm. If the rate at which the water flows into the tank is 8 km/h, find how long it takes to fill the tank. Answered by Penny Nom. 





Volume of a trough 
20001209 

From Matt: I have been given the information of the length of the trough, and the end pieces are isosceles triangles, and two equal sides of the triangle are given. I cannot seem to find the answer, nor anything in my book relating to the question. Answered by Harley Weston. 





Volume of a box 
20001115 

From A student: A box 3" wide and 2" deep is to have a volume of 2 cubic feet. How long must the box be? How many pieces of lumber are stacked in a pile 2" high if each board is 3/8" thick? Answered by Penny Nom. 





A trig question 
20000701 

From Will: An open rectangular tank a units deep and b units wide holds water and is tilted so that the base BC makes an angle theta with the horizontal. When BC is returned to the horizontal, who that the depth of the water is (a squared) * cot theta div 2b units Answered by Harley Weston. 





Volume of a sphere 
20000521 

From Kevin Partridge: Does anyone have a way to physically demonstrate how to explain the volume formula for a sphere? Or perhaps how to derive the formula without calculus? Answered by Harley Weston. 





Filling a hole 
20000401 

From John McNeill: I have an area 20 feet long and 12 feet wide It starts out at a depth of 4 inches and ends up at 0 inches. How much sand do I need to fill the excavation. Answered by Penny Nom. 





Surface area of a sphere 
20000322 

From Gina Wilkie: How can I demonstrate to my middle school students the reason for the formula for the surface area of a sphere? Answered by Walter Whiteley and Chris Fisher. 





Putting in a pool 
20000316 

From Katie: If your digging a hole for a pool and the pool is: Length= 11m Width= 6m Sallow Depth= 1.1m graduating to 'Deep' Depth= 1.8m What is the volume of soil that will be taken out? And if a bobcat can excavate and remove 10m3 (qubed) of soil an hour how long will it take him to excavate the soil. Answered by Penny Nom. 





The length of a cylinder 
20000217 

From Kelly Wichmann: What is the formula to figure the volume of a cylinder? We have a cylinder that is 2 3/4" in inside diameter and a gallon of oil that needs to fill it. We are trying to figure out how long the cylinder should be. Can you help us? Answered by Chris Fisher. 





Volume of an ellipsoid 
19991206 

From Michael Nowicki: I am a physician at the University of Mississippi. I am trying to compare the size of polyps (abnormal growth of tissue in the colon) between 2 groups of individuals. The department of pathology gives the size as length X width X depth  how do I calculate the volume? Polyps are nearly ovoid in shape. Answered by Walter Whiteley. 





Liquid capacity 
19990615 

From Bernard Antill: Would you please tell me how many litres of water in a swimming pool that is 24 feet long, 16 feet wide & 4 feet deep. I would appreciate you showing the formula for this calculation. I am a 74 year old male and I cannot find a formula in which I have any faith! I would also appreciate the answer in Imperial gallons. Answered by Penny Nom. 





Measuring the fourth dimension 
19990607 

From Suzanne Hall: Hi! The other day, two of my students asked a very interesting question: Is the fourth dimension measured with hypercubes? Their reasoning went like this: Lines are 1D and are measured with line segments, which are part of a line. Planes are 2D and are measured with squares, which are part of a plane. Space is 3D and is measured with cubes, which are part of space. So, logically, hypercubes would be used to measure the fourth dimension. Answered by Chris Fisher. 





Volume of oil in a tank 
19990417 

From Lars Waldemarsson: My problem is to get an equation for the depth of the oil in a gastank formed like a cylinder. The cylinder is in a horizontal position and by a stick you will be able to get the depth of the oil in the tank. All I need is an exmaple which I can build on. By this equation you will be able to get the volume of the oil if you know the depth. Answered by Harley Weston. 





Ounces and milliliters 
19990417 

From Tony Rizzi: I'm mixing a formula of: 48 oz distilled water. 15 grams of Hydroxy Ethyl Cellulose GR (powder) 30 grams of Hydroxy Ethyl Cellulose MR (powder) 200 grams of Barium Sulfate (powder) 1000 grams of Calcium Hydroxide (powder) After mixing, I need to estimate the amount of each ingredient that fits in a 3ml syringe. And how many syringes I can fill? Answered by Harley weston. 





Volume of a cube. 
19990404 

From Alex Elkins: How do you find the volume cubic matter of a cube or space, example how many cubic feet in an example 6" high 4' X 6' rectangle Thank You Answered by Penny Nom. 





Volume in gallons 
19981209 

From Hill Hermit: Please tell me the formula for computing the volume, in gallons, of a cylinder. Thanks from a parent. American gallons, please. Answered by Harley Weston. 





Platonic Solids Surface Area 
19981202 

From Rachel Bidwell: How do you find the surface area of the 5 platonic solids, when they each have a volume of one cubic inch Answered by Harley Weston. 





Volumes 
19980829 

From Lorraine Wall: Consider the region in the first quadrant bounded by the x and y axes, the vertical line x=3 and the curve y = 1 / (x squared + 3). Determine the volume of the solid by rotating this region about the xaxis. Now that is the first part. I then have to find the coordinates of the centroid of the solid by rotating this region about the xaxis. Thanks. Lorraine Answered by Harley Weston. 





Area and Volume 
19980728 

From James Pulver: I am going into 12th grade and am practicing for the SAT II. I have come across a problem that I cannot solve. It states that the front, side , and bottom faces of a retangular solid have areas of 24 square centimeters, 8 square centimeters, and 3 square centimeters, respectively. What is the volume of the solid. I need to know how to solve similar problems so is there a formula to go from area to volume? Answered by Jack LeSage. 





Volumes of Revolution 
19980724 

From Lorraine Wall: I'm on the section fpr The Computation of Volumes of Solids of Revolution and the following question is giving me problems: Consider the region in the first quadrant bounded by the xand yaxes, the vertical line x=3, and the curve y=1/(xsquared + 3) I can determine the volume of the solid by rotating the region about the yaxis using the shell method but I can't seem to be able to get started with the volume when rotated about the xaxis. Answered by Harley Weston. 





What is the volume of a regular tetrahedron? 
19961021 

From Paul Bleier: How does one calculate the volume and the height of a three sided pyramid formed by equilateral triangles? Answered by Bruce Gilligan. 





Volume d'une sphere entre 4 autres spheres 
20100118 

From Bonfils: Bonjour,
Je souhaiterais en fait calculer le rayon de la sphère max qui pourrait s'insérer entre 4 sphères de rayon connu.
Merci par avance pour votre réponse.
Sincères salutations Answered by Chris Fisher. 





Le volume d'une boule 
20091022 

From ve.lu.ch: Pour calculer le volume d'une boule, il faut utiliser la formule :
4/3 x Pi x R au cube
Pourquoi 4/3 ?
Merci d'avance Answered by PierreLouis Gagnon et Claude Tardif. 





Preuve du volume d'une boule 
20090406 

From Geneviève: J'aimerais avoir l'explication du volume de la boule, qui est (4pi R au cube) divisé par 3.
J'aimerais savoir le pourquoi de l'équation, la preuve de celleci.
Merci! Answered by PierreLouis Gagnon. 





Un volume d'une capacité minimal 
20090105 

From Pauline: je doit faire un volume d'une capacité minimal de 2500 cm 3 en quell matiere que ce soit
* un prisme a base pentagonale non réguliere
* une sphere
* stella octangula Answered by PierreLouis Gagnon. 





Le volume du tas 
20080528 

From ribot: je cherche la formule mathematique du volume d un tas de cailloux formule employée dans le bâtiment Answered by Thierry Moisan. 





Combien vais je avoir de surface ? 
20070522 

From Maëlle: J'ai 5m3 de terre et veux en mettre 5 cm partout pour faire un terrain de jeux. Combien vais je avoir de surface ? Answered by Claude Tardif. 





Mesure/volume 
20070509 

From Ashley: Calcule le volume des 2 contenants et quels est le plus grands. Answered by Claude Tardif. 





volume d'un cône 
20061129 

From Emmanuel: On peut diviser un cube en 3 pyramides et ainsi en déduire le volume d'une pyramide. Mais comment peuton déduire le volume d'un cône de celui d'un cylindre? Comment visualiseton la division d'un cylindre en trois? Answered by Claude Tardif. 





Volume d'un cône 
20060424 

From Christelle: Caroline décide de se servir de ses connaissances mathématiques pour "rouler" son petit frère: "Arthur, ditelle, je te propose que nous mettions chaucun un euro dans l'achat d'un cône glacé. Je mangerai la première, jusqu'à mihauteur, et toi, tu auras la seconde moitié."
Combien la part de Caroline représenteraielle par rapport à celle de son petit frère s'il acceptait ? Answered by Claude Tardif. 





les formules d'aire et de volume de les solides 
20030201 

From Annie: Je cherche le nom des mathématiciens qui ont découvert les différentes formules d'aire et de volume de tous les solides ( boule, cube, les prismes, cylindre, cône, pyramide, polyèdres réguliers). Je cherche aussi à trouver comment ils ont démontré l'exactitude de ces formules. L'important, c'est de connaître le nom des mathématiciens qui ont découvert ces formules. Answered by Claude Tardif. 





Volume d'une calotte ellipsoidale 
20021211 

From Fabien: Quel est le volume d'une calotte d'ellipsoide de hauteur h (ellipse de longueurs d'axes a, b, et c)? Je souhaite une formule exacte, un développement limité, voire une intégrale à estimer numériquement. Quelle méthode pour le calculer ? Answered by Claude Tardif. 





Le volume d'un ellipsoïde 
20010317 

From Lise: Je cherche à calculer le volume d'un ovoide, avezvous une formule? Answered by Claude Tardif. 





Le volume d'une sphère 
20000917 

From Pitmill: merci de me donner la formule pour trouver le volume d'une sphère. Answered by Harley Weston. 





Volume tetraedre 
19980213 

From Solecki Yannick: j`aimerais savoir s`il existe une formule de calcul simplifie pour trouver le volume du tetraedre en fonction de ses cotes et sans utiliser une expression matricielle. Answered by Chris Fisher. 

