# How do you use cylindrical shells to find the volume of a solid of revolution?

If the solid is obtained by rotating the region between the graph of $f \left(x\right)$ and the x-axis from $x = a$ to $x = b$ about the y-axis, the volume $V$ of the solid can be found by Shell Method:
$V = 2 \pi {\int}_{a}^{b} x f \left(x\right) \mathrm{dx}$