Math CentralQuandaries & Queries


Question from Justin, a student:

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? Please show formula as I am driving myself crazy with conversions. Please advise. Thanks.

Hi Justin,

The volume of a cylinder is

V = π r2 h

where r is the radius, h is the height and π is approximately 3.1416. I'm going to use yards and there are 36 inches in a yard so the inside diameter of the hose is 0.75/36 yards and the inside radius is 0.375/36 yards. The volume is 1 cubic yard so

1 = π (0.375/36)2 h

Solve for h. Once you have the height you can check using our volume calculator.


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