Answer
$\dfrac{64\pi}{3}$
Work Step by Step
Conversion of rectangular to cylindrical coordinate system gives $r^2=x^2+y^2 \\ \tan \theta=\dfrac{y}{x} \\z=z$
Let $I=\iiint_EZdV=\int_0^{2\pi} \int_{0}^{2}\int_{r^2}^{4} zr dr dz d\theta$
or, $I=\int_0^{2\pi} \int_{0}^{2}[\dfrac{z^2}{2}]_{r^2}^{4} r dr dz d\theta$
or, $I=\int_0^{2\pi} \int_{0}^{2}(8r-\dfrac{r^5}{2}) dr dz d\theta$
or, $I=\int_0^{2\pi}[\dfrac{8r^2}{2}-\dfrac{r^6}{12}]_{0}^{2} d\theta=\dfrac{64\pi}{3}$
