Answer
$$\dfrac{8\pi}{3}$$
Work Step by Step
Our aim is to integrate the integral as follows:
$$ Volume =\int^{2\pi}_0 \int^{\pi/2}_{\pi/3} \int^2_0 p^2 \space sin\phi dp \space d\phi \space d\theta \\=\dfrac{8}{3}\int^{2\pi}_0 \int^{\pi/2}_{\pi/3} \sin \phi d\phi \space d\theta \\=\dfrac{8}{3} \times \int^{2\pi}_0 [-\cos(\phi)]^{\pi/2}_{\pi/3} \space d\theta \\=\dfrac{4}{3} \times \int^{2\pi}_0 (1) d\theta \\=\dfrac{8\pi}{3}$$
