Math CentralQuandaries & Queries


Question from Michael:

Volume of earth moved @ 500' across, 1 to 3 degree slope, 30' deep X 50' across at the bottom.

Hi Michael.

The slope must be more than that. 30 feet deep and 500 feet across gives arctan(30/500) = 3.46 degrees from top to bottom. So it will depend on the profile of the gradient - perhaps most is 1-3 degrees and there is a drop at the bottom...?

Based on a straight slope of 3.46 degrees, you can calculate the volume by multiplying the length x width x depth and dividing by two (a wedge is half of a rectangle). So 500 x 30 x 50 / 2 = 375 000 cubic feet. There are 27 cubic feet (3^3) in a cubic yard, so dividing that out, you would have about 13 900 cubic yards of earth to move.

Hope this helps,
Stephen La Rocque



Stephen and I interpreted your question differently. Stephen took "30' deep" to mean the depth of the earth and I took it to mean the depth of the lot. In my interpretation you have a lot that is 500 feet across at the back, 50 feet across at the front and 30 feet deep. The lot slopes from front to back at 1 to 3 degrees.

Can you give us a more complete description of your situation with perhaps a photograph or a sketch?


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