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