Answer
$\dfrac{ 3a}{4}$
Work Step by Step
$Average=\dfrac{3}{4 \pi a^3} \int_0^{2\pi} \int_{0}^{\pi} \int_{0}^{a} \rho^3 \sin \phi d \ rho d \theta$
or, $=\dfrac{3a}{16 \pi} \int_0^{2\pi} \int_{0}^{\pi} \sin \phi \ d \phi \ d\theta$
or, $=\dfrac{3a}{8\pi} \int_0^{2\pi} d\theta$
or, $=\dfrac{3a}{8\pi} [2\pi-0] d\theta$
or, $=\dfrac{ 3a}{4}$
