Answer
$2\pi \space R \space h$
Work Step by Step
The formula to determine the surface area is as follows:
$S= \int_{m}^{n} 2 \pi y \sqrt {1+(\dfrac{dy}{dx})^2}$
Now, $ S=(2 \pi)\int_{a}^{a+h} [\sqrt {R^2-x^2}] [\dfrac{R}{\sqrt {r^2-x^2}}] dx \\=(2 \pi ) \int_{a}^{a+h} \space R \space dx\\= 2 \pi R (a+h-a)\\=2\pi \space R \space h$