Answer
$\dfrac{2a}{3}$
Work Step by Step
Our aim is to integrate the integral as follows:
$ Average =\dfrac{4}{\pi a^2} \int^{\pi/2}_0 \int^a_0 r^2 \space dr \space d\theta $
or, $=\dfrac{4}{3\pi a^2} \int^{\pi/2}_0 \space a^3 \space d\theta $
or, $=\dfrac{2a}{3}$
