







A pattern for a truncated cone 
20131220 

From Josh: I need to know how to layout a truncated cone with a base diameter of 18" a top
Diameter 15.25 and a height of 20". Your help will be greatly appreciated. Answered by Penny Nom with a spreadsheet by Don. 





Solving a cone 
20080129 

From Marija: [Note: this problem shows how to solve anything about a cone if you are given two measurements.]
Is there a formula for finding the diameter of the base of the cone? Answered by Stephen La Rocque. 





Pattern for a truncated cone 
20070511 

From Mike: I have been trying to get this cone flat so I can build this column. Can you please help me so I can figure this out? Thanks for your help. Answered by Stephen La Rocque. 





A sand castle in the shape of a truncated cone 
20200523 

From Summer: A sand castle is in the shape of a truncated cone as shown. Calculate the length of the diameter of the base.
The diameter of the top of the truncated cone is 20cm
The height is 30cm
The slopes are 32cm Answered by Penny Nom. 





Maximizing the volume of a cone 
20200518 

From Ella: Hello, this is question  'If you take a circle with a radius of 42cm and cut a sector from it,
the remaining shape can be curled around to form a cone. Find the sector
angle that produces the maximum volume for the cone made from your circle.' Answered by Penny Nom. 





The missing diameter of a truncated cone 
20200417 

From Brandon: Need a formula to find missing large Dia of a truncated cone where the small dia =.19" Height= 2" and taper =16deg Answered by Harley Weston. 





The volume of a coffee cup 
20200125 

From Amirah: What is the volume of a polystyrene cup with a height of 8cm, diameter of 5cm at the top and 4cm at the bottom when it is filled with water? Answered by Penny Nom. 





Volume of a tree 
20191219 

From Maria: I have trees for sale. I need to calculate the volume of a tree from base which is wider than the stem.The base will be used for the making of hurleys, similar to hockey sticks so the wider base is crucial. Answered by Penny Nom. 





A flat top cone 
20190825 

From Mary: I want to make a paper model of a flat top cone with the radius of the base is 12.5 cm and the radius of the apex is 7 cm.The height is 15 cm and the radius of the apex is 5 cm. The height is 15 cm.
Can you help me with the angle and construction, please?
Thanks. Answered by Penny Nom. 





A cone of maximum volume 
20190814 

From Refilwe: The slant height of a cone is 10cm. Determine the radius of the base so that the volume of the cone is a maximum Answered by Penny Nom. 





The maximum volume of a cone 
20190714 

From A student: find the maximum volume of a cone if the sum of it height and volume is 10 cm. Answered by Penny Nom. 





The top half of a cone 
20190227 

From danica: What portion of the height from top that the cone be cut into two equal volume? Answered by Penny Nom. 





An ice cream cone 
20190205 

From Eyuel: a scoop of ice cream has a 3inch radius how tall should the ice cream cone at the same radius be in order to contain all of the ice creams inside the cone Answered by Penny Nom. 





A cylinder with a cone on top 
20190116 

From Berania: A water tower in New York City has the shape of a cylinder with a cone on top. The cylinder has a diameter of 12 feet and a height of 15 feet. The roof has an inclination angle of 25 degrees.
(a) Determine the height of the cone to the nearest tenth of a foot.
(b) Determine the overall volume of the tower to the nearest cubic foot. Answered by Penny Nom. 





The top of a truncated cone 
20181202 

From Sameer: Bottom cone radius 1124.height is 200. Top radius 15degree decree to bottom radius. Top radius how much ? Answered by Penny Nom. 





Two cones formed from two circular sectors 
20181130 

From APARNA: The central angles of two sector of a circle are 60° and 120° . Using these sectors two cones are made. If the radius of the smaller cone is 5 cm, find the radius and base area of the larger cone. 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. 





Form a cone from a circle sector 
20180812 

From Tinashe: A 216 sector of a circle of radius 5cm is bent to form a cone. Find the radius of the base of the cone and its vertical angle. Answered by Penny Nom. 





Truncated cones 
20180808 

From Belgacem: Hello, I have a truncated cone: height 500mm , Base radius=147mm and I want to calculate the Top surface radius. How to do that? thank you Answered by Penny Nom. 





The area, radius and slant height of a cone 
20180518 

From joette: If you have a cone how to find the slant height when given the area and 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. 





A cone formed from a circular sector 
20180418 

From Jessica: A circle has a radius of 7.5cm. A sector with an angle of 240 degrees is cut out from the sector. If the sector is folded to form a cone. Find the length of the cone. 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. 





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. 





Forming a cone from a circle 
20170415 

From Tasha: A sector of a circle subtends an angle of 216 degrees at the centre, If this sector is used to form a cone of vertical height ,8cm, calculate the base radius of the cone Answered by Penny Nom. 





A cone inscribed in a hemisphere 
20160807 

From anonymous: A cone is inscribed in a hemisphere. the slant height of the cone is 20cm. When cut along its slant height, the cone forms a sector of a circle.
find the angle of the sector, to the nearest 1 decimal place. Answered by Penny Nom. 





The lateral side length of a cone 
20160605 

From Diane: Question is find the lateral side length of a right cone with area of 372 sq. cm and base circle radius of 9 cm. Answered by Penny Nom. 





A stained glass cone lamp 
20160409 

From Edwin: In making a 16" dia. cone lamp (stained glass), how many square feet of glass do I need. Answered by Penny Nom. 





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. 





The diameter of the top of a truncated cone 
20160124 

From Peter: I am trying to calculate the diameter of a truncated cone given
one diameter the height of the cone and a 10% taper from one end
to the other. For example a butter churn is 18" tall and 9" in
diameter at the base. the sides need to slope inward at 10%
What is the diameter at 9" and 18" Answered by Penny Nom. 





The height of a truncated cone 
20151204 

From Jack: I need to build a truncated cone that has a top of30 inches and a base of 64 inches . The sides need to be at a 64.5 degree angle. This will determine the height. Can this be calculated? Answered by Penny Nom. 





The intersection of a plane and a cone 
20150516 

From Tom: Is there a way to derive an equation that describes the perimeter of the intersection of a plane and a cone regardless of the angle of the plane to the cone. Assume that the plane does not cut through the base of the cone, the x, y, z location of the vertex is known, the distance from the vertex to the plane through the axis is know., and that the angle of the cone is known. Answered by Chris Fisher. 





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. 





Constructing a cone 
20150312 

From Levi: While the mathematics at the welding shop page was very helpful there is one vital part missing. If I have never built a cone how do I figure out how much bigger the diameter of my
circle has to be when laying flat on the floor verses the diameter when it has been pulled into a cone. Answered by Harley Weston. 





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. 





Largest cone in a sphere 
20150115 

From Alfredo: What is the altitude of the largest circular cone that may be cut out from a sphere of radius 6 cm? 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. 





Planar curves 
20141213 

From ann: what does planar curve mean in your definition of a cone? 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. 





A cone of vision 
20140429 

From David: It is known that a fish in water looking up has a 97 degree "cone" of vision that sees "through" the surface of the water. If a fish lies 4 inches below the surface, the cone forms a window (circle) smaller than if a fish lies 8 inches below the surface. What is the ratio of inches of depth to the radius of the circle on the surface that is its visual window? Answered by Penny Nom. 





Two cones 
20140409 

From c.j: what is the length of the radius of the LARGER cone(the LARGER cone has a slant height of 15) when the SMALLER cone has a radius of 8 and a slant height of 12ft ,please help. Answered by Penny Nom. 





A cone inscribed in a sphere 
20140228 

From joel: how can I find the radius and the height of a cone INSCRIBED in a sphere, given the sphere having a radius of 6? ( note: the diameter of the cone is equal to its slanted height). Answered by Penny Nom. 





The diameter of the base of a cone 
20140223 

From elwin: i have a sector of a circle that has 120 degree and 6 cm length. What will be the diameter of the base of the cone.
and what is the diameter of the angle is changed to 180. Answered by Harley Weston. 





The volume of a cone 
20140208 

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





A frustum 
20131012 

From Lily: A cone of height 6in. and radius of base 4in. has its top cut off by a plane parallel to its base and 4in from it.
Find the volume of the remaining frustum.
I have worked out the volume of the entire cone but I don't know how to work out the radius of the top of the frustum.
Thanks Answered by Penny Nom. 





Maximize the volume of a cone 
20131009 

From Conlan: Hi I am dong calculus at school and I'm stumped by this question:
A cone has a slant length of 30cm. Calculate the height, h, of the cone
if the volume is to be a maximum.
If anyone can help me it would be greatly appreciated.
thanks. Answered by Penny Nom. 





Slicing through a cone to form an ellipse 
20130806 

From Pulkit: we get an ellipse on slicing through a cone. Is there a relation between central axis of the cone and this ellipse?
Does it pass through the any of the foci of the ellipse? Answered by Chris Fisher. 





A cone problem 
20130414 

From Courtney: Hello,
I am having difficulty solving this cone problem. The biggest challenge I have is figuring out what angle they are talking about:
The angle at the base of a cone is 34.5 degrees. Find the diameter of the cone at point on the edge of the cone 26cm from the tip. Answered by Penny Nom. 





The height of a sheet metal cone 
20130209 

From Charles: Sheet metal cone.
I need a cone with a finished base of 38.19719 diameter
The cone is to be from a 48 diameter round with the wedge cut out.
The best calculation I have is the arc is 286.479. (correct?)
Could you verify this arc angle but more so what is the cone height? Answered by Harley Weston. 





How many edges does cone have? 
20130128 

From Meriem: how many edges does cone have pls? Answered by Lorraine Dame, Chris Fisher and Walter Whiteley. 





A label to cover a plastic cup 
20121023 

From Kevin: I'm trying to make a label to cover the entire outer area or a plastic cup. I know there must be a way to figure out the dimensions needed, but I can't seem to figure it out. The circumference of the bottom of the cup is 21.4cm and the circumference at the top of the cup is 29.8cm. The cup is 14.5cm tall. What should the height of the arc from the plane connecting the two ends of the 21.4cm arc. I attached a diagram where x is the value I'm looking for. I'm guessing there is some simple relationship between the length of a line and the arc needed to turn that line into a perfect circle, but I don't know what it is. Can you figure this out and share it with me? Thanks.
Kevin Answered by Penny Nom. 





Cones, pyramids, cylinders and prisms 
20120913 

From Roy: I read on this page that a pyramid is a special kind of cone, but a cone is not a pyramid. Does this apply to cylinders. Is a prism a special kind of cylinder, but a cylinder is not a prism? Answered by Robert Dawson. 





Making a wind sock 
20120828 

From John: I am trying to build a wind sock and need to be able to lay the shape
out on cloth. I need the wind sock front opening (diameter) to be
3 1/2" and the rear opening diameter to be 1". The windsock needs
to be 9 1/2" long. I tried using the example of the person trying to
make a crayfish trap but got confused and could not figure out my
numbers. Any help would be greatly appreciated.
Thanks
John Answered by Penny Nom. 





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 truncated cone: the central angle 
20120717 

From Tom: I have researched several sites, including this one and am fairly confident I can do the calculations required to produce the two radii and the slant height for a truncated cone.
I a somewhat confused by the central angle. Some sites indicate that it should never exceed 180 degrees while others do not. Different examples on your site seem to use this in two different ways in constructing a truncated cone.
Sometimes the angle seems to indicate the section to be removed, while in other examples the angle seems to indicate the section to be saved. Since the two angles will always total 360 I am confused about how to use the info to
calculate the minimum rectangle required to contain the pattern. I'm guessing that in some cases I may need to use the chord or sagitta to determine the desired height and width of the material. Any help is greatly appreciated.
Thank you.
Tom Answered by Penny Nom. 





A lamp shade 
20120515 

From Fleur: I am helping my child make a cone lampshade, the measurements are as follows in "cm's"
21 cm = height
8 cm = top diametre
40 cm = bottom diametre
Please could you give the pattern (cut out) dimensions for final cut. Answered by Penny Nom. 





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. 





The dimensions of a conical tent 
20120304 

From yash: a conical tent is to accommodate 11 people.Each person must have 4m square of space on the ground and 20m cube at air to breathe.Find the height and radius of the conical tent.26202 Answered by Penny Nom. 





Building a tipi 
20120129 

From Lacy: Hi there!
We are building a tipi for our children. We want to build a large one about 15ft tall with a base of about 15 feet diameter. I am trying to figure out how much canvas we need to accomplish this. I graduated about 20 years ago and am struggling. Please help if you can. 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. 





Water is flowing into a cup 
20111219 

From Tim: A cup has a radius of 2" at the bottom and 6" on the top. It is 10" high. 4 Minutes ago, water started pouring at 10 cubic " per minute. How fast was the water level rising 4 minutes ago? How fast is the water level rising now? What will the rate be when the glass is full? Answered by Penny Nom. 





A pattern for a cone 
20110830 

From Izzy: I need to create a cone as a prop and my math is not good enough to create the pattern.
Here are my instructions :
The diameter is 2'5" and it has to be 4 feet tall. It is a giant cone. I want it to be pointy at the end, not truncated. Answered by Penny Nom. 





A cone with an oval as a base 
20110803 

From Emily: Hi, I was wondering how to calculate the surface area of a cone with an oval as a base (which I think is referred to as an elliptic cone or something like that). I have the both the maximum and minimum radius as well as the height, but I don't have a slant height and I'm not sure how to calculate it and then calculate surface area. I would really appreciate some help. Thanks! Answered by Robert Dawson. 





Cone story problem 
20110416 

From Chelsea: There is a cone with a story problem that states only that the radius is the same as the altitude and that the slant height of the cone is 6cm. I have no idea how to figure this problem out. 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. 





A conical container and a spherical balloon 
20110406 

From Steven: Water is running out of a conical container 12 feet in diameter and 8 feet deep (vertex down) and filling a spherical balloon.
At the instant the depth of the water in the cone is 4 feet, the radius of the sphere is approximately 4 feet.
The rate of change of the depth of the water in the cone at the instant is approximately ______________ times the rate of change of the radius of the balloon. Answered by Penny Nom. 





At what rate is the grain pouring from the chute? 
20110226 

From MJ: Suppose that grain pouring from a chute forms a conical heap in such a way that the height is always 2/3 the radius of the base. At the moment when the conical heap is 3 m high, its height is rising at the rate of 1/2 m/min. At what rate (in m^3/min) is the grain pouring from the chute? Answered by Penny Nom. 





Cutting the top off a conical tent 
20110222 

From tom: how far from the top must you cut a conical tent in order to cut the
cloth in half... Answered by Penny Nom. 





Making a truncated cone 
20110218 

From lisa: We need to make a cone that has the following dimensions.
143/8" diameter on large end
133/8" diameter on small end
4" tall
What are the dimensions I need to cut in order to make a cone with one seam? Answered by Stephen La Rocque. 





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. 





A cone with a specific angle 
20110201 

From John: Hi my daughter came with a seemingly easy question (which to me it was not)
How to make/calculate a cone of a specific angle from top to bottom radius. Answered by 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. 





A truncated cone 
20101231 

From jagjeet: dear suppose i have cone of 50cm radius at base and 100cm radius at top at a height of 80cm. now keeping base radius of 50cm and height of 80cm i want to increase top radius to 150cm how will i do that. plz height m talking abt is vertical height not slant height 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. 





A play tent 
20100628 

From Susan: Hi!!!
I am making a play tent as seen at the link below and need to figure out how to get the dimensions for the cone shape. The one shown has 4 different seams, but I guess I can get away with just one seam to sew it together (?) I need it to go over a hula hoop as that is what I am using for the round support at the top. My hula hoop is
35" in diameter from outside edge to outside edge. I would like the height of the teepee to be around 30" from the center to the peak.
Thanks so much, oh my gosh, I have been fretting for 2 days about this and my hair is about to fall out!!!!
Please contact me if you need any additional info.
~Susan
http://www.landofnod.com/family.aspx?c=52&f=4100 Answered by Penny Nom. 





Volume of a styrofoam cup 
20100623 

From Stacy: how do you find the volume of a truncated cup with height of 3, top diameter of 2.5, and a bottom diameter of 2 Answered by Penny Nom. 





More on a truncated cone 
20100528 

From Mike:
Question from Mike, a parent:
I was reviewing this question and answer:
http://mathcentral.uregina.ca/QQ/database/QQ.02.06/phil1.html
But I have trouble with this part:
Now if we express the radius of the inside circle as r and the outside circle's radius is R, then this means r/R is 911/1728. But earlier we said that the outside radius R is simply w more than the inside radius r, so R = r + 282. That means that r/R = r/(r + 282). Now we can simply solve the equation for r:
r/(r+282) = 911/1728
This means r = 314 mm (with rounding).
Can I get more detail on the method to solve for r?
Thank you,
Mike Answered by Penny Nom. 





The "vertex" of a cone 
20100427 

From Tom: By definition a vertex is a point where three edges meet in a 3 dimensional object.
My ten year old son argues that the point at the top of a cone is not a vertex since it does not fit the definition. He got the answer wrong on a test recently but insists that he is right. I need a mathematician to answer this for him. Answered by Robert Dawson and Chris Fisher. 





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. 





A max min problem 
20100406 

From Terry: The vertex of a right circular cone and the circular edge of its base lie on the surface of a sphere with a radius of 2m. Find the dimensions of the cone of maximum volume that can be inscribed in the sphere. Answered by Harley Weston. 





A 3D cardboard cupcake 
20100130 

From Margaret: Hi,
I'm an art student and I'm attempting to build a 3D cupcake out of cardboard.
I want it to have a circular base of 8.5 inches and sides that are 7'' tall and slope outward so the top of the base is 29'.
The top with the frosting would be a detachable lid made from a cone with a base circumfrance of 29".
My problem is how to cut the side so they will slope out, I'm pretty sure there needs to be a curve, however I don't how to calculate the degree of it.
Ideally I want the sides to be a single piece of cardboard.
I also don't know how to calculate the arc needed to make a cone who's circular base's circumfrence is 29''.
Thanks,
Margaret Answered by Stephen La Rocque. 





A cone circumscribed about a given hemisphere 
20100119 

From Neven: The cone of smallest possible volume is circumscribed about a given hemisphere. What is the ratio of its height to the diameter of its base?
(G.F.Simmons, Calculus with Analytic Geometry, CH4 Applications of Derivatives) Answered by Chris Fisher. 





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. 





A pile of sand 
20091216 

From Malik: Sand is leaking out of a hole at the bottom of a container at a rate of 90cm3/min. As it leaks out, it forms a pile in the shape of a right circular cone whose base is 30cm below the bottom of the container. The base radius is increasing at a rate of 6mm/min. If, at the instant that 600cm3 have leaked out, the radius is 12cm, find the amount of leakage when the pile touches the bottom of the container. Answered by Harley Weston. 





A truncated cone 
20091111 

From Lucian: I need to calculate the bottom inside diameter of a truncated cone.
The top insdie diameter is 1450mm.
The material is 6mm thick
The cone angle is 20 degrees
The slant length is 152mm
I would like a formula so that I can build a spread sheet Answered by Penny Nom. 





Making a cone 
20090819 

From angela: how can i make a cone with a 6cm of heigth and has 2cm radius in the opening?? Answered by Stephen La Rocque. 





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. 





A cone with the top cut off 
20090802 

From Paul: I am making a cone with a diameter of 1300, a base of 500, a side length
800. I need to workout so I can draw it out flat, cut it out, and make into
a cone. Answered by Harley Weston. 





The lateral area of a cone 
20090715 

From ashley: What is the radius of a cone with the lateral area being 443.3 mm^2 and the slant height being 14.7 mm. Answered by Penny Nom. 





Find out the length of a cup when its volume is halved 
20090525 

From Thomas: I'm having trouble with a question.
What kind of formula would i use to find out the length of a cup when its volume is halved? Answered by Stephen La Rocque. 





The dimensions of a larger cup 
20090523 

From Elizabeth: Hey
If i have a cup that holds a volume of 477mL and the bottom radius is 2.8cm and the top radius is 4.9cm and the height is 10cm. If i increase the volume by one and a half times what is the new measurements if the cup is directly proportional to the first one.
Thank you Answered by Stephen La Rocque and Penny Nom. 





The volume of a cone 
20090520 

From Lillian: okay! so my math question is about the volume of a cone! my work sheet gave me the volume and base of the cone and asked me for the height! please help me discover the height of a cone when the volume is 78.54 cm (cubed obviously) and the base is 6 centimeters. thanks so much :) Answered by Penny Nom. 





12 oz. cup 
20090419 

From Tom: I am a ceramic teacher and wanted my students to make a 12 oz. cup, what formula should we use? Answered by Chris Fisher. 





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. 





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. 





A conical sleeve 
20090217 

From Jonathan: I'm having a hard time making a design pattern for a cone sleeve, the thing is the cone sleeve is 22 degrees, how can i know the angle of this when it is flat on paper, based on my calculations, it should be around 66  69, but i want it to be exact can anybody help? Answered by Penny Nom. 





A sphere in a cone 
20090210 

From Shubham: An upturned conical vessel of radius 6cm and height 8cm is completely
filled with water. A sphere is lowered in the conical vessel filled with
water and the size of sphere is such that it just touches the sides of
cone and is just immersed. What fraction of water overflows? Answered by Harley Weston. 





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. 





Water flowing from a cone to a cylinder 
20090123 

From Ray: Water is passing through a conical filter 24 cm deep and 16 cm across the top into a cylindrical container of radius 6 cm. At what rate is the level of water in the cylinder rising when the depth of the water in the filter is 12 cm its level and is falling at the rate of 1 cm/min? Answered by Harley Weston. 





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 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. 





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 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. 





Related rates 
20081126 

From Lyudmyla: How fast is the volume of a cone increasing when the radius of its base is 2 cm and growing at a rate of 0.4 cm/s, and its height is 5 cm and growing at a rate of 0.1 cm/s? Answered by Harley Weston. 





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 conical funnel 
20081112 

From Rachael: Hello, I am a 10th grader in AP Calc, and can not figure out this question:
Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top. Answered by Harley Weston. 





Water is leaking from a conical tank 
20081024 

From Kimberly: Water is leaking out of an inverted conical tank at a rate of 12000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank. Answered by Stephen La Rocque. 





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. 





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 cardboard spaceship 
20080831 

From Lee: I am building a "cardboard" spaceship for my 4 year old grandson.
The cabin is a dishwasher box with a cool control panel and elipse shaped
windows.
I really need help designing the cone or"nosecone".
The diameter of the base is 26", 24" tall, with a 6" diameter opening
at the top.
Thank you for the help!
Lee Answered by Penny Nom. 





A cone on the end of a cylider 
20080805 

From Jerry: Hi.
I need to make a plastic cone to fit on the end of a cylinder. The only dimension i have is the diameter of the cylinder.
This 553 mm.
I need to find the formulae required and how much material will be required. Answered by Penny Nom. 





A cube inscribed in a right cone 
20080716 

From Steven: A cube is inscribe in a right cone of radius 2 and height 5. What is the volume of the cone? Answered by Victoria West and Harley Weston. 





How many face does a cone have? 
20080621 

From Vanessa: How many face does a cone have? Answered by Harley Weston. 





Liquid is being pored into the top of a funnel 
20080525 

From Stella: Liquid is being pored into the top of a funnel at a steady rate of 200cm^3/s. The funnel is in the shape of an inverted right circular cone with a radius equal to its height. It has a small hole in the bottom where the liquid is flowing out at a rate of 20cm^3/s. How fast is the height of the liquid changing when the liquid in the funnel is 15cm deep?
At the instance when the height of the liquid is 25cm, the funnel becomes clogged at the bottom and no mo re liquid flows out. How fast does the height of the liquid change just after this occurs? Answered by Stephen La Rocque. 





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. 





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. 





Smallest cone containing a 4cm radius inscribed sphere 
20071219 

From Eva: A sphere with a radius of 4cm is inscribed into a cone. Find the minimum volume of the cone. Answered by Stephen La Rocque. 





The vertex of a cone 
20071118 

From miriam: how many verticies does a cone have Answered by Penny Nom. 





Cones and pyramids 
20071110 

From Eric: I have a question regrading the differences between a cone and a pyramid.
In my son's Maths workbook, a cone is always referred to as a pyramid,
which confuses me very much. I understand that a pyramid is a special case of a
cone and therefore you can refer a pyramid as a cone but not the other way around.
Am I correct? Answered by Harley Weston. 





Stanley Cup costume (truncated cone pattern) 
20071019 

From Janet: You hockey fans will love this question. I am making a Stanley Cup halloween costume and need a flat pattern for the bowl portion. I believe a truncated cone will work nicely. Base circumference needs to be 32" (10.19 diameter). Top circumference needs to be 44" (14 diameter). It needs to be 8" high. Thanks for your help. Answered by Stephen La Rocque. 





Surface area of an openended cone 
20071016 

From Lorne: What is the surface area of an open ended cone? Measured at 10' high,
16' diameter on the bottom and 2' diameter at the top. Answered by Stephen La Rocque. 





Size of a sphere fitting inside a cone 
20070927 

From Juan: I am supposed to find the largest sphere that
will fit into a cone. I am assuming is a maximizing problem, but I am not sure
of what relation (between a cone and a sphere) to use. Answered by Penny Nom and Stephen La Rocque. 





Solving an equation with fractions 
20070920 

From Len: I am having a brain cramp or maybe I just forgot some basic math,
but I am having trouble solving for "r" in your truncated cone example
where r/(r+w)=r/R or r/(r+282)=911/1728. Could you refresh my memory
by showing the steps to solve for "r"? Answered by Harley Weston. 





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. 





A truncated cone 
20070824 

From JUAN: i need to create a template for a cone that has a 4 " opening at top, a 14" base and 12" tall.Can u tell me how to achieve this ?
u have similar problems but when i try to do it , is not coming up right , please help.. Answered by Harley Weston. 





A cone with two fruits 
20070726 

From Meg: You have a cone shaped bag. At the bottom of the bag is an orange with
radius r. On top of the orange is a melon with radius R. It touches the
orange and fits snugly in the bag, touching it in a ring around the orange.
Its top is at the same level as the top of the bag. What is the radius of the
cone? 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. 





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. 





Lateral area of a right cone 
20070517 

From Crystal: In my homework the question says the lateral area of a right cone is 226.08 cm cubed.
the slant hieght is 12 cm. Find the total surface area. How do I do that? 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. 





Is the point on a cone called a vertex? 
20070509 

From Felicia: Does a cone have a vertice? My teacher says that a vertice can only be
made if two or more edges join up at an angle, so what do you call a point on a cone? Answered by Walter Whiteley. 





Slicing a doublenapped cone with a plane 
20070507 

From Andrew: I am writing a paper about creating parallel lines by slicing a doublenapped cone with a plane. I have found out how it can be shown by algebra that the equations for parallel lines are generated from the degenerate case of a second degree polynomial in two variables, but I have yet to find a source with a visual representation of this case. Do you know if it exists? Answered by Chris Fisher. 





The radius of a cone 
20070507 

From Braden: i need to find the surface area but i only have the slant height and the height i need the radius how do i find it? Answered by Penny Nom. 





Maximize the volume of a cone 
20070427 

From ashley: hello,
I've been stumped for hours on this problem and can't quite figure it out.
The question is: A tepee is a coneshaped shelter with no bottom. Suppose you have 200
square feet of canvas (shaped however you like) to make a tepee. Use
calculus to find the height and radius of such a tepee that encloses the
biggest volume.
Can you help?? Answered by Stephen La Rocque and Penny Nom. 





How do i form a paper cone 
20070414 

From Sash: How do i form a paper cone with the height of 25 cm, the slant height
of 25.8 cm, and the radius of 6.2 cm? Answered by Stephen La Rocque. 





A "claw setting" for a gemstone 
20070330 

From Stephanie: I'm trying to make a cone out of a flat sheet of metal for a "claw setting" for a gemstone.
The cone must be 8mm wide at the top and 11mm long tapering to a point. But because the prongs must be cut out of the top the cone should not start to taper for a length of 3mm from that top 8mm. The 3mm prong is then bent over the 8mm stone. That probably doesn't make enough sense. But I don't know how to explain it. If it helps a claw setting is the very common prong setting for engagement rings or earrings. Please help as soon as possible as this is a commissioned piece for someone and I'm running out of time. I don't remember any math really from high school so please make the instructions really easy to follow. Thank You!! Answered by Penny Nom. 





A truncated cone 
20070310 

From Russell: Hello, I have attempted to use two of your answers already given and had no real success. This young lady is making a cat food dispenser using a truncated cone. The top of the cone as a diameter of 5 inches with a height of 6 1/2 inches and diameter of 3 inches for the bottom.
Could you please map out a solution for the both of us to understand? Thank you so much for your time and for this wonderful service.
Russell Answered by Penny Nom. 





The volume of a styrofoam cup 
20070308 

From leanna: find the volume of a styrofoam cup if the diameter of the top is three inches, the diameter of the base is 2 inches, and the height is 4 inches. Answered by Penny Nom. 





A metal shroud for a outdoor fireplace 
20070306 

From Arnold: I am making a metal shroud for a outdoor fireplace, it is basically a lampshade type pattern,like the bottom of a cone.The top has to be 6 inches to fit the 6 inch stovepipe,and the bottom will be a 24 inch circle. the sides will be 18 inches in length.With the cost of the sheet metal,I can only afford to cut this out once,can you help me with the pattern ? Answered by Penny Nom. 





A long narrow cone 
20070304 

From Amy: I am an art student making a piece of jewelry out of a flat metal sheet. I'm trying to make a long narrow cone that's roughly 3 1/4" long and just slightly under 1" wide at the base. Since I'm no math wiz, I'm having a really hard time. Please help. Answered by Penny Nom. 





The lateral area of a cone 
20070227 

From Michael: Ive seen the other question about surface areas. I still don't understand the lateral area. In my math book, it has (pi * r * L) as the equation, r = radius and L = height of the cone. This is 8th grade math. Thanks. Answered by Penny Nom. 





The radius of a cone 
20070226 

From lee: hi i have a cone to calculate, the height and radius are equal and the slant height is 0.5m
the total surface area is 15m sq i need to calculate the radius of the cone Note : this will lead to a quadratic equation could somebody have a look please Thanks Lee 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. 





Surface Area of a cone 
20070219 

From Cari: I am doing a math project. I am very confused on how to find the surface area of a cone. I have looked at other equtions but i still don't understand. How do you find the surface area of a cone that has a 15cm length and a 3.5cm radius? 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. 





Two cones 
20061230 

From Cassie: A cone of radius 6 and height 12 and a different cone of radius 8 and height 12 intersect as shown in the figure below, where the vertex of one matches with the center of the base of the other. Find the volume of the intersection of the two cones (in exact form). Answered by Penny Nom. 





Wheat is poured on a conical pile 
20061117 

From Rachel: wheat is poured through a chute at the rate of 10 cubic feet per minute and falls in a conical pile whose bottom radius is always half the altitude. how fast will the circumference of the base be increasing when the pile is 8 feet high? Answered by Penny Nom. 





Motorcycle expansion chamber design 
20061114 

From David: I'm interested in calculating cone information regarding motorcycle expansion chamber design for example. I guess it's called a truncated cone, from what I've read so far. If I know the center line height, small radius, and large radius of a truncated cone then, how can I calculate the angle (included angle?) the cone forms? I'd like to know the variations of the formula so I can calculate for angle, or length, or one of the diameters if I know the other two measurements. Answered by Stephen La Rocque. 





Constructing a cone 
20060920 

From Suresh: i want to know the required size of plate for cone rolling,sizes are 2950mm is bottom dia,894 is top dia and 600 is height.I have already read u r answers but i little bit confused ,harely and sue have given useful answers but when i worked both method the required plate size is different. so i like to know which method is easy and correct.and also i like know whether it can be rolled without segment my rolling machine width is 1500. Answered by Penny Nom. 





The radius of a cone 
20060908 

From Hermanson: I know the cone is 20 degrees at the top and 80 degrees at the bottom. What is the formula for finding the radius? Answered by Stephen La Rocque. 





How fast is the water level rising 
20060812 

From Erin: Water runs into a conical tank at the rate of 9ft^{3}/min. The tank stands point down and has a height of 10 ft. and a base radius of 5 ft. How fast is the water level rising when the water is 6 ft. deep? (V=1/3 pi r^{2} h). Answered by Penny Nom. 





Pyramids and cones 
20060606 

From Melissa: I was wondering if a cone can be considered a pyramid. Looking at many definitions of pyramids I have read that pyramids come to a common vertex. A cone comes to a vertex. But I also read that pyramids all have triangular faces. In this case a cone would not be considered a pyramid. Am I correct? Answered by Chris Fisher. 





A truncated cone 
20060528 

From Phil: Hi, I am an art student and I am trying to make a "truncated cone" (ie: a cone with the top cut off) out of sheet metal. I need to design a template first and am having problems working out the angles. The truncated cone is 250mm high, 550mm wide at the bottom and 290mm wide at the top. Can you help? Answered by Stephen La Rocque. 





Pythagorus and cone dimensions 
20060426 

From Glynnis: How do you find the measure of a side that is not the hypotenuse using the Pythagorean Theorem? Also, how do you figure the surface area and volume of a cone when the radius is 5 yards and the height is 8 yards? Answered by Stephen La Rocque. 





What is the surface area of a cone with a hemisphere on top? 
20060420 

From Jordan: How do you find the surface area of a cone with a hemisphere on top? The only information I have is the radius of the hemisphere, which is 4, and the total height, which is 7. Answered by Stephen La Rocque. 





Cone dimensions 
20060412 

From Mirnela: The height of a cone is 40 and the radius is 9. How
do I find the slant height of this?
Also, how do I find the area of the base of a cone if the radius is 7?
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. 





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. 





A lampshade shape 
20060211 

From Rose: Is there a solid shaped like a lampshade? Or do you just call it the bottom portion of a cone? Answered by Penny Nom. 





A sheet metal cone 
20051205 

From Laura: I am an art student and in the process of making a cone out of sheet metal. I am unable to work out the template I need to produce my final cone. The dimensions I have are that the final cone will be 58mm high and will have a diameter of 102mm. Answered by Penny Nom. 





A pattern for a truncated cone 
20051204 

From Nick: I need to make a large cone segment. The large end has ID of 57 inches and the small end has ID of 23 inches. The cone is essentially a 45 degree cone (90 degrees at the tip). The sides of the segment are 2 feet long. How do I lay out a flat pattern that will fold into this segment? I need to know radius 1 and radius 2 and the angle the piece must be. Answered by Penny Nom. 





A truncated cone 
20051203 

From Sonny: I need to create a template for a cone that has a 2" opening at the top, a
4" base and stands 6" tall. Can you tell me how to achieve this? Answered by Penny Nom. 





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 slump cone 
20051027 

From Wendy: we are trying to make a slump cone (used to measure the slump in concrete). It has dimensions of 8" diameter on the bottom, 4" diameter hole on the top and a height of 12".
Please help, it is getting frustrating. Answered by Penny Nom. 





A conical hat 
20051022 

From Manish: I need to make a conical hat for my daughter's upcoming fancy dress, the circumference of the base(hollow) is 50 cms,the height of the cone is 30 cms,what should be the dimensions of the paper which will make a cone of the beforementioned dimensions? Answered by Penny Nom. 





A cone with vertex (1,1,2) 
20050926 

From Brandon: Find the equation of a double cone with vertex (1,1,2) and which intersects the xy plane in a circle of radius 4. 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. 





Surface areas 
20050511 

From Jessica: How can I demonstrate to my high school students the reason for the formulas for the surface area of a prism, right cylinder, and regular pyramid, and right cone? Answered by Penny Nom. 





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. 





Construction of a cone 
20041120 

From John: I am a builder working on a project where I need to make a cone. It's a right circular cone with 15" base radius and slant angle of 30 degrees. I want to cut it out of flat sheet metal then bring the edges together to form the cone. Is this enough information? Answered by Penny Nom. 





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. 





Constructing a cone 
20040907 

From Steve: I am trying to build crayfish traps; one of the components is a cone shaped entry section.
The cone I want to make would be 12" in diameter at the base and 12" in height, from base to peak.
I need a formula to calculate the dimensions and a method of transferring the shape onto a flat piece of material.
Answered by Harley Weston. 





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. 





An elliptic cone 
20040224 

From Ben:
I am building a model for my architecture class. I need to build a elliptic cone out of chipboard and i have no idea how to do this.
The cone needs to be 20in tall and the ellipse has a max radius of 10in and a min radius of 8in.
So my question is how do i lay this out on a piece of paper so that i can form the cone after i cut it out.
Answered by Penny Nom. 





The vertex of a cone 
20040129 

From Richard: Please help me explain to my fourth graders as to why a cone has a vertex even though it does not have any straight edges. Answered by Chris Fisher. 





Making a cone 
20031222 

From Tracie:
I am working on a craft project at home and I have been given the following information: 16" tall and 13" diameter at base, with 1 and 1/2 " opening at top.
Is there a basic formula for creating a cone with this info?
Answered by Claude Tardif and 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. 





A sphere inscribed in a cone 
20030810 

From A student: A sphere with radius 5cm is inscribed in a right circular cone 20 cm in height.find
(a) the base radius ,volume of the cone (b)volume of the shaded space( to 3 sig fig) Answered by Penny Nom. 





The vertex of a cone 
20030327 

From Holly: I read your response to Callie about whether a cone has a vertex or not. Is it ONLY a vertex if both halves of the cone are together or can one half of the illustration have a vertex? Answered by Walter Whiteley. 





A lampshade from a cone 
20021126 

From Ellsie: I need to make a pattern to cover an old lampshade. This is actually the bottom portion of a cone. Please help me figure out how to draw this pattern, so that we can complete our project. Answered by Penny Nom. 





A cone that is cut off at the top 
20020923 

From Stuart: I have to work out the dimensions and arcs of a cone that is cut off at the top. I.e Top diameter is 33mm to bottom diameter is 43mm and the depth is 80mm Are you able to work what the flat of this cone would be as I need to design within the flat area and then have it cut out. I really need to know what the flat of it is before it is cut and curled to form the above cone. Answered by Walter Whiteley. 





A paper model of a cone 
20020814 

From Bruce: I have made a paper model of a cone, cut a sloping section, and removed the top. I have drawn the major and minor axis on the paper surface of the section. The major axis is not symmetrical about the minor axis. To me, this is not an ellipse. To me, an ellipse is a tubular section, because this gives a symmetrical major axis. What is your opinion? Answered by Walter Whiteley and Chris Fisher. 





Conics 
20020529 

From Brooke: Which conic cannot be generated by an intersection of a plane and a double napped cone? Answered by Chris Fisher. 





The vertex of a cone 
20020413 

From Callie: Does a cone have a vertex? Answered by Penny Nom. 





A cone in 3 space 
20020320 

From Matthew: Let C in R^{3} be the cone defined by x^{2} + y^{2}  z^{2} = 0 (A) Let P be the plane described by x + 2z = 1 (i) Find a description of P in terms of two parameters s and t . . . Answered by Walter Whiteley. 





Water in a conical tank 
20011020 

From Sarah: The problem: Water flows into a conical funnel at a continuous rate of one gallon per minute (One gallon = 231 Cu.In.). The height of the funnel is 5" and the diameter is 8". The 1st formula: I need to develop a formula that will give the volume, in cubic inches, of the water in the funnel at any time t (in seconds). V = f(t). The 2nd formula: I need to develop a formula that will give the height of the water in the funnel at any time t (in seconds). h = f(t). 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. 





Faces 
20010221 

From Sandy: How many faces are there on a sphere? What are the faces of a cone? What is the definition of a "face" of a 3D object? Answered by Walter Whiteley. 





Making a paper cone 
20000730 

From John: The question of how to lay out & cut out of paper, cones came up. I would like the cone have : A base of 4 inches and height of 4 inches, 6 inches, 8 inches. 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. 





Lining a cone 
20000406 

From Jim Campbell: I am not a student, I am trying to solve a business problem. The question. If I want to put a lining in a chute that is cone shaped, how do I calculate the size steel plate I need to do that. The cone is 10' in diameter at the top and has a 20" hole at the bottom. The total height of the chute is 8'. Answered by Harley Weston. 





Slant height of a cone 
20000224 

From Jocelyn Wozney: I need help with this problem for my high school calculus class. Any help you can give me will be greatly appreciatedI am pretty stumped. "Express the volume of a cone in terms of the slant height 'e' and the semivertical angle 'x' and find the value of 'x' for which the volume is a maximum if 'e' is constant. Answered by Harley Weston. 





Surface area of a cone 
19990918 

From Frothy: I don't understand how to find the surface area of a cone. The height is 12cm and the radius is 5cm. Answered by Walter Whiteley. 





Some Calculus Problems. 
19971030 

From Roger Hung:
 What real number exceeds its square by the greatest possible amount?
 The sum of two numbers is k. show that the sum of their squares is at least 1/2 k^2.
 .
. . Answered by Penny Nom. 





Formulae for Surface Area. 
19970428 

From Gary Millward: I'm trying to help my son with his Math homework (Grade 10) and he has to find the surface area of a cone and rectangluar pyramid. We have the formulas for the volume of these solids, but can't seem to locate the formulas for surface area. Answered by Walter Whiteley. 





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. 

