Moment of inertia about z is calculated as $\displaystyle \int\int\int_{{E}}{\left({x}^{{2}}+{y}^{{2}}\right)}\rho{\left({x},{y},{z}\right)}{d}{V}$ where $\displaystyle \rho$ is the density function.

Let $\displaystyle {E}$ be the solid below $\displaystyle {z}={50}-{x}^{{2}}-{y}^{{2}}$ and above the square $\displaystyle {\left[-{5},{5}\right]}\times{\left[-{5},{5}\right]}$

Given the solid has a constant density of 6, find the moment of inertia of $\displaystyle {E}$ about the z-axis.