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| Math Central | Quandaries & Queries |
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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.
Penny
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