Chapter 6: Applications of Definite Integrals - Section 6.1 - Volumes Using Cross-Sections - Exercises 6.1 - Page 322: 19

$\dfrac{ 32 \pi}{5} $

We integrate the integral to calculate the volume as follows: $V= \int_{0}^{\pi/2} \pi x^4 dx$ Now, $V=(\pi)\times [\dfrac{x^5}{5}]_0^2$ or, $=(\pi)(\dfrac{(2^5)}{5}-0)$ or, $= (\pi/8)[\dfrac{\pi}{2}-0]$ or, $=\dfrac{ 32 \pi}{5} $