Math CentralQuandaries & Queries


Question from Roger, a student:

I used the volume formula and found that a cylinder with a 3" radius X 8.75" height yields just over 231 cu. in. (one gallon)- doesn't seem right, but that's what I got. Then found the percent that 8.175" is to one foot and multiplied that into the number of feet in 20 miles. I'm not good at math, so I'm starting to lose myself here. The short story is I get a cylinder that is 20 miles long and only .0000387" in diameter. Is this even close to the mark?

Hi Roger,

I also got 231 cubic inches. (I used a radius of 8.175 inches. Is that what you have?)

The volume V of a cylinder is given by V = π r2 h where r is the radius and h is the height. You have a volume of 231 cubic inches and a height of 20 miles and you are looking for the radius. First convert 20 miles to inches, There are 5280 feet in a mile and 12 inches in a foot so 20 miles is 20 × 5280 × 12 inches. Thus

231 = π r2 × 20 × 5280 × 12.


r2 = 231/(π × 20 × 5280 × 12)


r = √[231/(π × 20 × 5280 × 12)] = 0.0076 inches.


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