# Chapter 7 - Applications of Integration - 7.3 Exercises - Page 462: 3

$\frac{128\pi}{5}$

#### Work Step by Step

Setup the integration using shell method $2\pi \int_0^4 x(\frac{1}{4}x^2)dx$ $2\pi \int^4_0 x^{\frac{3}{2}} dx$, Integrate $2\pi (\frac{2}{5}x^{\frac{5}{2}})]_0^4$, Take definite integral $2\pi ((\frac{64}{5})-0)$ $\frac{128\pi}{5}$

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