Answer
$$\dfrac{ 32 \pi}{5} $$
Work Step by Step
We need to integrate the integral to compute the volume.
$$Volume = \int_{0}^{\pi/2} \pi x^4 \space dx \\=\dfrac{(\pi) x^5}{5}]_0^2 \\=(\pi)(\dfrac{(2^5)}{5}-0) \\= (\dfrac{\pi}{8})[\dfrac{\pi}{2}-0] \\=\dfrac{ 32 \pi}{5} $$
