## Calculus 8th Edition

$\dfrac{162\pi}{5}$
$z=9-x^2-y^2$ and $z=9-r^2$ For cylindrical coordinate system: $I=\int_0^{\pi} \int_{0}^{3}\int_{0}^{9-r^2} (r) \times (r)\times dz dr d\theta$ $=\int_0^{\pi} \int_{0}^{3} [r^2z]_{0}^{9-r^2} \times dr d\theta$ $=\int_0^{\pi} \int_{0}^{3} r^2(9-r^2) \times dr d\theta$ $=\int_0^{\pi} \int_{0}^{3} (9r^2-r^4)dr d\theta$ $=\int_0^{\pi} [3r^3-\dfrac{r^5}{5}]_{0}^{3} d\theta$ $=[\dfrac{162\theta}{5}]_0^{\pi}$ $=\dfrac{162\pi}{5}$