# Volumes by Cross Sections

Volumes by Cross Sections can be setting a unit volume, $\delta V$ of a cross section. Then establish an integration for evaluating the volume of the entire solid.

### Worked Examples of Volumes by Cross Sections

The base of a solid is formed by the area bounded by $y = \cos x$ and $y = -\cos x$ for $\displaystyle 0 \le x \le \frac{\pi}{2}$. Vertical cross sections of the solid taken parallel to the $y$-axis are in the shape of isosceles triangles with the equal sides of length 1 unit. Find the volume of the solid.