Answer
$384 \pi$
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 $I=\iiint_E\sqrt{x^2+y^2} dV=\int_0^{2\pi} \int_{-5}^{4}\int_0^{4} r^2 dr dz d\theta$
or, $I=\int_0^{2\pi} d\theta \int_{-5}^{4} dz \int_0^{4} r^2 dr$
or, $I=[\theta]_0^{2\pi} [z]_{-5}^{4} [\dfrac{r^3}{3}]_0^{4}$
or, $I=(2\pi)(4+5) \times [\dfrac{1}{3}(4)^3-0]=384 \pi$
