Answer
$32\pi$
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_0^4 \frac{1}{4}x^3 dx $
$2\pi (\frac{1}{16}x^4)]^4_0$, Integrate
$ 2\pi ((16)-0)$ , Take definite integral
$32\pi$
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