







A cylindrical water tank with a leak 
20170601 

From Alexander: if a cylindrical water tank has diameter of 90cm and leak starts at the bottom 10 litres in an hour. how long will it take for the level to fall by 20cm Answered by Penny Nom. 





A 2 million gallon tank 
20160928 

From Kimberly: I have a tank that is shaped like a cylinder, and it has to hold 2 million
gallons of water. There is a height limit of 30 ft.
I know the equation is V=pi x r squared x h but I don't know if I need anything
For the square foot of water. 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. 





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. 





A region described by inequalities in cylindrical coordinates 
20150221 

From Rahul: I am not able to visualize a solid given by inequalities as under (in cylindrical coordinate system)
0=
I know that (can visualize) first 2 inequalities say it is a cylinder of infinite length.
It seems that third inequality poses the restriction to the height as well as it makes us to remove a cone.
But I just can not understand it clearly.
Thanks in advance!
Regards,
Rahul 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. 





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. 





The height of a cylindrical container 
20120410 

From Rodney: a cylindrical container has a radius of 6cm. the container is holding 255 cm3 of water. rounded to the nearest quarter inch, what is the minimum height of the container? Answered by Penny Nom. 





A cylindrical container 
20120214 

From KRIS: YOU ARE PaCKAGING 4 EQUAL SIZED PAINT CANS WITH A RADIUS 8CM AND A HEIGHT OF 20CM, IN A CIRCULAR CONTAINER.What is the surface area of the packing container? Answered by Penny Nom. 





A cylindrical tank 
20110116 

From tom: A cylindrical tank, 1 ft in diameter, length 6 ft , is placed so that its axis
is horizontal. How many pounds of water will be used in filling it to a depth
of 9in. , if water weighs 62.4 lbs. per cu. ft.? Answered by Penny Nom. 





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. 





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 cylindrical vessel with belled ends 
20100601 

From George: surface area of a vessel with a cylindrical length of 60 feet, a diameter of 10 feet, and with belled ends of 5foot radius Answered by Penny Nom. 





Cutting a pipe at an arbitrary angle 
20080920 

From John: from the original question Al asked about cutting a 200 diameter pipe in 45 degrees. can someone explain the math steps required to creating the graph. I am trying to do the same thing only using a 150 degree cut. Answered by Harley Weston. 





Gasoline in a cylindrical tank 
20080525 

From Simon: A cylindrical tank with height 15m and diameter 2m is being filled with gasoline at a rate of 500L/min. At what rate is the fluid level in the tank rising?(1L = 1000cm^3). About how long will it take to fill the tank? Answered by Penny Nom. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





Intersection of perpendicular cylindrical surfaces 
20010731 

From Charlie: Please consider two right circular cylinders, perpendicular one to the other, and of unlike radii in a 3 dimensional Cartesian space with mutually perpendicular x,y,z axes. If one cylinder is centered on the y axis with radius ra, and the other on the z axis with radius rb, then the expression for the first surface would be x^{2} + z^{2} = ra^{2}, y = any number. Likewise, the second cylinder's surface would be x^{2} + y^{2} = rb^{2}, z = any number. It is my intent to define the curve at the intersection of these two cylindrical surfaces. From sketching the conditions it appears that this intersection resembles an ellipse folded about its minor axis. Answered by Chris Fisher. 

