Math CentralQuandaries & Queries


Question from Bryan, a student:

How many cubic yards of aggregate must be ordered for a road base 16 in. thick and 2 miles long with a top width of 30 ft, if the side slopes are one on one, or 45 degrees

Hi Bryan.

The area of the cross section times the length of the road base will give you the volume needed.

The cross section is a trapezoid (the top and bottom are parallel lines). The area of a trapezoid is (1/2)(h)(a+b) where h is the height between the parallel sides, and a and b are the lengths of the parallel
sides. If a is the top, then it is just 30 ft.

You'll need to calculate the length of the bottom of the road base. To do that, remember that a 45 degree angle means that the length extensions (on each side), the slope and the depth form a right isosceles triangle, so the length extension is the same as the depth.

Hope this helps. Keep your units straight!

Stephen La Rocque

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