Answer
$$\dfrac{3}{4}$$
Work Step by Step
Our aim is to integrate the integral as follows:
$$ Average=\dfrac{1}{(\dfrac{4\pi}{3})}\int^{2\pi}_0 \int^\pi_0 \int^1_0 p^3 \sin(\phi) \space dp \space d\phi \space d\theta\\=\dfrac{3}{16\pi}\times \int^{2\pi}_0 \int^{\pi}_0 \sin\phi d\phi \space d\theta \\=\dfrac{3}{8\pi} \times \int^{2\pi}_0 (1) d\theta\\=\dfrac{3}{4}$$
