## Thomas' Calculus 13th Edition

$V=2\int^{\pi}_{\pi/2} \int^{-3cos\theta}_0 \int^r_0$ dz r dr $d\theta$ =$2\int^{\pi}_{\pi/2} \int^{-3cos\theta}_0 r^2 dr$ d $\theta$ =$\frac{2}{3}\int^{\pi}_{\pi/2} (-27cos^3\theta) d\theta$ =$-18([\frac{cos^2\theta\sin\theta}{3}]^\pi_{\pi/2}+\frac{2}{3}\int^\pi_{\pi/2}cos\theta d\theta)$ =12