Math CentralQuandaries & Queries


Question from curtis, a parent:

If I was to pile 3.5 cu. yds of dirt around a 5ft 6in. diameter cylinder within 24in. of the outside, how high will the dirt be?

Hi Curtis,

Is this what you have in mind?


The units are inches. 5 feet is 60 inches so the radius of the inside cylinder is 66/2 = 33 inches.

The volume of a cylinder is π r2 h where r is the radius and h the height. The volume of dirt is the volume of a cylinder of radius 33 + 24 = 57 inches and height h inches minus the volume of a cylinder of radius 33 inches and height h inches, that is

π 572 h - π 332 h = π h (572 - 332).

But this is in cubic inches and you have the volume of dirt as 3.5 cubic yards. There are 36 inches in a yard and hence 363 cubic inches in a cubic yard. Hence

363 × 3.5 = π h (572 - 332).

Solve for h.


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