Answer
$4 \pi a^2$
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_{-a}^{a} \sqrt {a^2-x^2} \times \sqrt {\dfrac{a^2}{a^2-x^2} } dx $
or, $ =(2 \pi)\int_{-a}^{a} a dx $
or, $=2 \pi a (x)_{-a}^a$
or, $=4 \pi a^2$
