Expert: Sherry Wallin - 6/26/2009

Question
Dear Ms. Wallin
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, yes of course I will explain how to change cubic feet into cubic inches. There is 12 x 12 x 12 cubic inches in 1 cubic foot, i.e., there is 1728 cubic inches in one cubic foot. So 9 cu feet has 9 x 1728
= 15552 cubic inches in it. So 15552 = π * (13.75)^2 * h = π * 189 * h, thus h = 15552/(π *189) where h is in inches!

Math Prof