Answer
$\frac{768\pi}{7}$
Work Step by Step
Setup the integration using shell method about the x-axis
$ 2\pi \int_0^8 y(\sqrt[3] y) dy$
$2\pi \int_0^8 y^{\frac{4}{3}} dy$, Integrate
$2\pi [\frac{3}{7}y^{\frac{7}{3}}]_0^8$, Take definite integral
$\frac{768\pi}{7}$ Simplify
