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 Question from Steve: I need your help please, I am looking to purchase some top soil and keep getting conflicting answers. There are 3 piles and here are the sizes; Pile #1: 203 feet around and 21.29 feet high. Pile #2: 195 feet around and 18.75 feet high. Pile #3: 150 feet around and 17.98 feet high. I look forward to hearing back from you asap. Thank You! Steve

Hi Steve,

The shape of each pile is approximately a cone and you can use the expression for the volume of a cone to find its volume. We have done precisely that in our response to an earlier question. There is however an easier procedure.

The volume of a cone of radius $r$ units and height $h$ units is

$\pi \; r^2 h \mbox{ cubic units.}$

The volume of a cylinder with the same radius and height is

$\frac13 \pi\; r^2 h \mbox{ cubic units.}$

Hence the volume of the cone is one third the volume of the cylinder. My suggestion is that for each of your plies you use our volume calculator at

http://mathcentral.uregina.ca/volume_calculator

to calculate the volume of the cylinder with the dimensions you supplied and then divide by 3 to find the volume of the conical pile. You can use the example in the first paragraph of my response to check that you are using the procedure correctly.

Harley

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