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