   SEARCH HOME Math Central Quandaries & 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.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.