# Chapter 6 - Applications of the Integral - 6.3 Volumes of Revolution - Exercises - Page 304: 7

$\frac{24573 \pi}{13}$

#### Work Step by Step

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

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