Answer
$\frac{2a}{3}$
Work Step by Step
We calculate the average as follows:
average=$\frac{1}{\pi a^2} \int^{a}_{-a} \int^{\sqrt{a^2-x^2}}_{-\sqrt{a^2-x^2}} \sqrt{x^2+y^2} dydx $
=$\frac{1}{\pi a^2} \int^{2\pi}_0 \int^a_0 r^2dr d\theta $
=$\frac{a}{3\pi }\int^{2\pi}_0 d\theta $
=$\frac{2a}{3}$
