# How do you find the volume of the solid with base region bounded by the triangle with vertices (0,0), (1,0), and (0,1) if cross sections perpendicular to the x-axis are squares?

##### 1 Answer
Jun 3, 2015

Start with a picture of what we are dealing with:

So we have a pyramid, the volume of which is given by the formula

$V = \frac{1}{3} \text{ base "xx" height}$

Volume of given shape $= \frac{1}{3}$

If you are uncertain of where the formula for the volume came from, consider the following image:

The pyramid (in red) with volume $3 v$ is equal to $\frac{1}{3}$ of the volume of the containing cube.