Math CentralQuandaries & Queries


Question from Roger, a parent:

I have an 18 foot round hole which is 16 inches deep. I want to fill the hole up with dirt. How much dirt do I need to fill the hole??

Hi Roger,

By an "18 foot round hole" I assume you mean an 18 foot diameter. Thus the hole has the shape of a circular cylinder. The volume is then π r2 d where r is the radius and d is the depth. If you are ordering dirt you will need the volume in cubic yards (contractors call them yards) so change all the units to yards. There are 3 feet in a yard so the 18/2 = 9 foot radius is 9/3 = 3 yards. There are 36 inches in a yard so the hole is 16/36 yards deep. Thus the volume is

π × 32 × 16/36 = 12.6 cubic yards.


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