Question

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

Answer 1

If a surface is obtained by rotating about the x-axis the polar curve `r=r(theta)` from `theta=theta_1` to `theta_2`, then its surface area A can by found by

`A=2pi int_{theta_1}^{theta_2}r(theta)sin theta sqrt{r^2+[r'(theta)]^2} d theta`.

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I hope that this was helpful.