Answer
$$\dfrac{2a}{3}$$
Work Step by Step
Our aim is to integrate the integral as follows:
$ Average=\dfrac{1}{\pi a^2} \times \int^{a}_{-a} \int^{\sqrt{a^2-x^2}}_{-\sqrt{a^2-x^2}} \sqrt{x^2+y^2} \space dy \space dx $
or, $=\dfrac{1}{\pi a^2} \times \int^{2\pi}_0 \int^a_0 r^2 \space dr \space d\theta $
or, $=\dfrac{a}{3\pi } \times \int^{2\pi}_0 (1) d\theta $
or, $=\dfrac{2a}{3}$
