Answer
$2\pi rh$
Work Step by Step
Our aim is to integrate the integral to compute the surface area. In order to solve the integral, we have:
$Surface \space Area(S_A)= (2 \pi)\int_{a}^{b} y \sqrt {1+(\dfrac{dy}{dx})^2}$
or, $ =(2 \pi)\int_{a}^{a+h} \sqrt {R^2-x^2} \times \dfrac{r}{\sqrt {r^2-x^2}} dx $
or, $=(2 \pi ) \int_{a}^{a+h} r dx$
or, $= 2 \pi r (a+h-a)$
or, $=2\pi rh$
