Answer
$\frac{64\pi}{5}$
Work Step by Step
Setup the integration using shell method about the x-axis
$2\pi \int_0^4 y(\frac{1}{2}\sqrt y)dy$
$\pi \int_0^4 y^{\frac{3}{2}} dy$ , Integrate
$ \pi[\frac{2}{5} y^{\frac{5}{2}} ]_0^4$, Evaluate the definite integral
$ \frac{64\pi}{5}$
