## Thomas' Calculus 13th Edition

$\frac{31\pi}{6}$
$V=\int^{2\pi}_0 \int^{\pi/2}_0 \int^2_ {cos\phi} p^2 sin \phi dp d\phi d\theta$ =$\frac{1}{3} \int^{2\pi}_0 \int^{\pi/2}_0 (8-cos^3\phi) sin\phi$ $d\phi$ $d\theta$ =$\frac{1}{3}\int^{2\pi}_0 [-8cos\phi+\frac{cos^4\phi}{4}]^{\pi/2}_0 d\theta$ =$\frac{1}{3}\int^{2\pi}_0 (8-\frac{1}{4})d\theta$ =$(\frac{31}{12}(2\pi))$ =$\frac{31\pi}{6}$
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