Expert: Paul Klarreich - 6/26/2009

Question
Dear Mr. Klarreich
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
Questioner:   Alfredo
Country:  United States
Category:  Advanced Math
Private:  No
 
Subject:  Volume calculation
Question:  Dear Mr. Klarreich
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
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Hi, Alfredo,

I think all you have to do is make everything be inches.  One cubic foot is 12^3 = 1728 cubic inches, and 9 cubic feet is 15552 cubic inches.  In that case your problem becomes:

I want to make a mixing drum with a volume of 15552  cu.in. The volume of a cylinder is V= π * radius squared * height. I know π, the volume (15552 cu. in.) and the radius (13.75 inches) and I am looking for the height.

NOW pretend you never heard of feet (or yards or anything else) and do the example.  Lengths are all inches; areas are all square inches, and volumes are cubic inches.  Inches and other measures work just as well for round objects as for straight ones.