Math CentralQuandaries & Queries


Question from Joel:

I am constructing a french drain 100 feet long x 6 inches wide by 18 inches deep. Within this trench will be a 4" diameter pipe which will be surrounded by washed gravel. How many yards of gravel do I need? Thanks!

Hi Joel.

The volume of the pipe is the volume of the cylinder 100 ft long with a 4" diameter (2" radius).
That's 1200 x 3.14159 x 22 = 15080 cubic inches.

The volume of the drain is the volume of the "box" that is 100 ft long by 6 inches by 18 inches.
That's 1200 x 6 x 18 = 129600 cubic inches.

The difference between these will be the volume of gravel you need. Thats 129600 - 15080 = 114520 cubic inches.

Since 36 inches = 1 yard, (36 inches)3 = (1 yard)3, so 363 cubic inches = 1 cubic yard.

By dividing then, we get the number of cubic yards of gravel: 114520 / (363) = 2.45 cubic yards.

Stephen La Rocque.>

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