Answer
$\pi r \sqrt {r^2+h^2} $
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_{0}^{h} \dfrac{r \space x}{h}\times \sqrt {\dfrac{r^2+h^2}{h^2} } dx $
or, $ =\int_0^h \dfrac{2 \pi r \sqrt {r^2+h^2} }{h^2} (x) dx$
or, $=|\dfrac{\pi r \sqrt {r^2+h^2} (x^2) }{h^2} ]_0^h$
or, $=\pi r \sqrt {r^2+h^2} $
