Math CentralQuandaries & Queries


Question from bev, a parent:

I have a pile of soil that is 284' around and 12' high. I need to know how many yards are in that pile. And then how do I convert that to cubic yards

Hi Bev,

I can approximate the volume of your pile of soil. I think it is approximately a cone with height 12 and the base a circle with a circumference of 284'. The circumference of a circle is 2 π r where r is the radius so

284 = 2 π r and hence r = 284/(2 π) = 45.2 feet.

Before I find the volume of the cone I want to convert the measurements to yards so that I obtain a volume in cubic yards. There are 3 feet in a yard so your conical pile has a base radius of 45.2/3 yards and a height of 12/3 yards. The volume of a cone is 1/3 π r2 h where r is the radius and h is the height. Thus the volume of the conical pile is

1/3 π (45.2/3)2 × (12/3) = 951 cubic yards.

Contractors use the term yards to mean cubic yards so your pile of soil is approximately 951 yards.


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