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