Textbook Problem

Find the exact volume of the solid that results when the rectangular region with vertices at $\left(\mathrm{0,\; 0}\right)$, $\left(\mathrm{6,\; 0}\right)$, $\left(\mathrm{6,\; 4}\right)$ and $\left(\mathrm{0,\; 4}\right)$ is revolved about the

a) $x$-axis

b) $y$-axis