   SEARCH HOME Math Central Quandaries & Queries  Question from Jeff: Hi my water tank is 10ft long and 45" around, can you tell me how many gallons it holds. thankyou jeff Jeff,

The volume of a cylinder is

π r2 h

where r is the radius, h is the height, or length it its lying down, and π is approximately 3.1416. The length and radius need to be in the same units and I am going to use inches since I know that 1 US gallon is 231 cubic inches.

There are 12 inches in a foot so the length of the tank is 120 inches. Is your tank really 45 inches around or is it 45 inches across?

The circumference of a circle (the distance around) is given by 2 π r so if your tank is 45 inches around then

2 π r = 45

and hence

r = 22.5/π = 7.16 inches

Thus the volume is

π × 7.162 × 120 cubic inches.

If the tank is 45 inches across then r = 45/2 = 22.5 inches and the volume is

π × 22.52 × 120 = 190851.75 cubic inches.

Once you have the volume in cubic inches divide by 231 to obtain the volume in gallons.

190851.75/231 = 826.2 gallons

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.