## Thomas' Calculus 13th Edition

$\frac{2a}{3}$
We calculate the average as follows: average=$\frac{4}{\pi a^2} \int^{\pi/2}_0 \int^{a}_0 r\sqrt{a^2-r^2}drd\theta$ =$\frac{4}{3\pi a^2}\int^{\pi/2}_0 a^3 d\theta$ =$\frac{2a}{3}$