Math CentralQuandaries & Queries


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!

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

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.


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