Math CentralQuandaries & Queries


Question from tom:

digging a pond 100ft by 70ft by12ft with a 2:1 side slope. how many cubic yards will be removed

Hi Tom,

If I understand correctly your pond will be 100 feet by 70 feet on the surface. All 4 sides slope inwards at a rate of 2 feet for each foot of depth.The depth is 12 feet so each side will move inwards 2 × 12 = 24 feet Thus the bottom of the pond will measure 100 - 2 × 24 = 52 feet by 70 - 2 × 24 = 22 feet.

I used some calculus and found the volume of the pond to be 44,256 cubic feet. There are 3 feet in a yard and hence 33 feet3 in a yard3. Thus you will need to remove 44,256/33 =44,256/27 = 1639.1 cubic yards of dirt.


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