Answer
$\pi r \sqrt {r^2+h^2} $
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_{0}^{h} \dfrac{r \space x}{h}\times \sqrt {\dfrac{r^2+h^2}{h^2} } dx \\=|\dfrac{\pi r \sqrt {r^2+h^2} (x^2) }{h^2} ]_0^h \\=\pi r \sqrt {r^2+h^2} $
