# How do I find the surface area of a solid of revolution using polar coordinates?

If a surface is obtained by rotating about the x-axis the polar curve $r = r \left(\theta\right)$ from $\theta = {\theta}_{1}$ to ${\theta}_{2}$, then its surface area A can by found by
$A = 2 \pi {\int}_{{\theta}_{1}}^{{\theta}_{2}} r \left(\theta\right) \sin \theta \sqrt{{r}^{2} + {\left[r ' \left(\theta\right)\right]}^{2}} d \theta$.