Math CentralQuandaries & Queries


Question from Michael:

How many tons of dirt are in a triangle 14M x10M x 8.1M x .8M deep?

Hi Michael,

The volume of dirt is the area of the triangle times the depth. You can find the area of the triangle using Heron's Formula. I got $39.78 m^2$ and hence the volume is $39.78 \times 0.8 = 31.82 m^{3}.$ The weight of this amount of dirt depends on the density of the dirt. I found a useful table of densities on the Engineering ToolBox site. Once you have chosen the correct type of dirt multiply the density in $kg/m^3$ to get the weight in kilograms. If you want the weight in tons you can ask Google. Just type x kilograms in tons into the Google search window, where x is the weight of the dirt in kilograms.


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