   SEARCH HOME Math Central Quandaries & 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.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.