   SEARCH HOME Math Central Quandaries & Queries  Question from Ray: Hello, ** I am wanting to add 2 French Drain's in my yard. The 1st drain will be 25 ft. long, 8 in wide and 18 in deep. The pipe I'm using is 4in. in diameter. I'm trying to figure out how many yards of clean gravel I will need for this project? ** The 2nd French Drain will be 100 ft in Length, 10in wide and 18 in deep. I will also be using the 4in in diameter pipe for this drain. I am needing to see how many yards of clean gravel, I'll need for this drain? Hi Ray,

First drain:

The volume of the empty trench is the area of the end times the length If you convert all the units to feet the area of the end of the trench is

$\frac{8}{12} \times \frac{18}{12} \mbox{ square feet}$

and hence the volume of the empty trench is

$\frac{8}{12} \times \frac{18}{12} \times 25 = 25 \mbox{ cubic feet.}$

To calculate the volume of gravel you need to subtract the volume of the pipe. The volume of the pipe is also area of the end times the length. The end is a circle of radius 2 inches or $\large \frac{2}{12}$ feet and hence the volume of the pipe is

$\pi \; \left(\frac{2}{12}\right)^2 \times 25 = 2.18 \mbox{ cubic feet.}$

Thus the volume of gravel you need is $25 - 2.18 = 22.82$ cubic feet.

To convert this to cubic yards you can use the internet. You can type What is 22.82 cubic feet in cubic yards? into the Google search window, I'm a Mac user so I would say

Hey Siri what is 22.82 cubic feet in cubic yards?

The calculations for the second drain are analogous.

Write back if you need more assistance,
Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.