Answer
$$12$$
Work Step by Step
Our aim is to integrate the integral as follows:
$$ Volume =(2) \times \int^{\pi}_{\pi/2} \int^{-3cos\theta}_0 \int^r_0 \space dz \space r \space dr \space d\theta \\ (2) \int^{\pi}_{\pi/2} \int^{-3 \cos\theta}_0 \space r^2 \space dr \space d \theta\\=\dfrac{2}{3} \times (-27) \times \int^{\pi}_{\pi/2} ( \cos^3\theta) d\theta \\=-18([\dfrac{\cos^2\theta\sin\theta}{3}]^\pi_{\pi/2}+\dfrac{2}{3} \int^\pi_{\pi/2} \cos\theta \space d\theta) \\=12$$
