Math CentralQuandaries & Queries


Question from Kathy:
I need to fill a hole that is 24 feet round x 12 inches deep. How much dirt will I need?


I'm assuming that by "24 feet round" you mean 24 feet in circumference. First find the radius by solving

C = 2 pi R.

For landscaping purposes 3 is a good enough approximation to pi, so

R ~ C/(2x3) = 4 feet

Once you have R, the formula for the volume of a cylinder is

V = pi x R squared x h ~ 3 x 4 x 4 x 1 = 48 cubic feet

Now divide by 27 [3x3x3] to convert into cubic yards, the usual unit by which you order soil. Round up to the nearest half cubic yard and ask the supplier for "two yards" of soil.

(If this is not a practical landscaping problem but a school problems your instructor will probably want more precision. Substitute 3.1416 for pi instead and forget the cubic yards bit.)

Good hunting


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