Math CentralQuandaries & Queries


Question from Chassity:

The gravel pile is 120' around at the base and goes up 20' high at the peak. How many tons or yards of gravel in that pile?


Let's look for the correct expression first. I know that the volume of a cone with base radius r units and height h units is given by

V = 1/3 π r2 h cubic units,

and I know that the circumference of a circle of radius r units is given by

C = 2 π r units.

Solving this last equation for r and substituting in the volume expression I get the volume as

V = (C2 h)/(12 π) cubic units.

Since you want the volume in cubic yards I would convert the measurements to yards. There are 3 feet in a yard so 120 feet is 120/3 = 40 yards and 20 feet is 20/3 = 6.67 yards. Hence the volume of the gravel pile is approximately

V = (402 × 6.67)/(12 π) = 283 cubic yards.


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