Answer
$128\pi$
Work Step by Step
Setup up the integration using shell method about the x-axis
$2\pi \int_0^4 y(16-y^2)dy$
$2\pi \int_0^4 (16y-y^3)dy$, Integrate
$2\pi [ 8y^2 - \frac{1}{4}y^4]_0^4$, Take the definite integral
$ 2\pi ((128-64) - 0)$, Simplify
$128\pi$
