Chapter 5 - Applications of Integration - 5.3 Volumes by Cylindrical Shells - 5.3 Exercises - Page 382: 11

$\displaystyle{V=192\pi}\\$

$\displaystyle{V=\int_{0}^{8}(2\pi y)\left(y^{\frac{2}{3}}\right)\ dy}\\ \displaystyle{V=2\pi\int_{0}^{8}y^{\frac{5}{3}}\ dy}\\ \displaystyle{V=2\pi\left[\frac{3}{8}y^{\frac{8}{3}}\right]_{0}^{8}}\\ \displaystyle{V=2\pi\left(\left(\frac{3}{8}(8)^{\frac{8}{3}}\right)-(0)\right)}\\ \displaystyle{V=192\pi}\\$