Math CentralQuandaries & Queries


Question from Terry:

One company is selling topsoil by the yard and another by the ton, how do I determine how many tons, 15 yards of top soil is?

Hi Terry,

It depends on the density of the topsoil they are selling. I found a table that may help somewhat, but the density in pounds per cubic foot varies from 78 to 125 pounds per cubic foot. (Look in the table under earth.) If you know the density you can calculate the weight in tons of 15 cubic yards. Let me take a density of 100 pounds per cubic foot as an example.

There are 3 feet in a yard so

100 lb/ft3 = 100 lb/ft3 × 33/1 ft3/yd3 = 2700 lb/yd3.

Since there are 2000 pounds in a ton this is 2700.2000 = 1.35 tons per cubic yard and thus 15 cubic yards weighs 1.35 × 15 = 20.25 tons.

This may give you a rough idea for a comparison of the costs from the two companies but you should probably call the second company and ask them how much it will cost for 15 yards of topsoil.


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