Expert: Ahmed Salami - 6/26/2009

Question
Dear Mr. Salami
I want to make a mixing drum with a volumetric capacity of 9 cu.ft. I found that the formula to calculate the volume of a cylinder is V= π * radius squared * height. I know π, the volume (9 cu. ft.) and the radius (13.75 inches) and I am looking for the height. The problem that I have is that the radius is in inches and the volume is in cubic feet so when I try to solve for Height I found a disparity that I think is due to this difference in units. I have been investigating online but all the examples that they give to convert inches into cubic inches is with a cube and that of course is straight forward length * width * height; but I cannot find anything like that using a cylinder. Can you please explain to me what would be the way to find the height in my problem? Thank you so much

Answer
Hi Alfredo,
You need to realise that the conversion for a cylinder is done exactly as you would for a cube. We're only interested in units here and if the units of length, width and height are in inches then the volume of a cube would simply be in (inches).(inches).(inches) = cubic inches. If you consider a cylinder, you would also find that if the radius and height are in inches then the unit of the volume would be (inches)^2 . (inches) = cubic inches.
For the problem where volume is in cu.ft and radius is in inches, you have to decide what you want the unit of height to be. If we want it to be in ft we simply convert the radius value from inches to ft and then get the height directly in ft. If we wanted the height in inches we convert the volume value from cu.ft to cu.in
1 ft = 12 inches
1 cu.ft = 1728 cu.in

I hope i have helped you.

Regards