Chapter 6: Applications of Definite Integrals - Section 6.1 - Volumes Using Cross-Sections - Exercises 6.1 - Page 322: 20

$\dfrac{128 \pi}{7} $

We integrate the integral to calculate the volume as follows: $V= \int_{0}^{\pi/2} \pi x^6 dx$ Now, $V=(\pi)\times [\dfrac{x^7}{7}]_0^2$ or, $=(\pi)(\dfrac{(2^7)}{7}-0)$ or, $=\dfrac{128 \pi}{7} $