Answer
$\frac{24573 \pi}{13}$
Work Step by Step
The volume is given by
$$
\pi \int_{1}^{8}\left(x^{5 / 3}\right)^{2} d x=\pi \int_{1}^{8} x^{10 / 3} d x=\left.\frac{3 \pi}{13} x^{13 / 3}\right|_{1} ^{8}=\frac{3 \pi}{13}\left(2^{13}-1\right)=\frac{24573 \pi}{13}.
$$
