Answer
$\frac{192\pi}{5}$
Work Step by Step
Setup the integration using shell method about the line x=6
$2\pi \int_0^4 (6-x)(\sqrt x)dx$
$ 2\pi \int_0^4 (6x^{\frac{1}{2}} - x^{\frac{3}{2}})dx$, Integrate
$2\pi [4x^{\frac{3}{2}} - \frac{2}{5}x^{\frac{5}{2}}]_0^4$, Evaluate the definite integral
$ 2\pi (32-\frac{64}{5})$
$\frac{192\pi}{5}$
