Answer
$$\dfrac{2 \pi}{3}$$
Work Step by Step
We need to integrate the integral to compute the volume.
We have:
Area $=R^2\pi- r^2 \pi=\pi (1-x^2)$
$$Volume = \pi \times \int_{0}^{1} (1-x^2) \space dx \\= \pi [x-\dfrac{x^3}{3}]_{0}^{1} \\= \pi (1-\dfrac{1}{3} -0) \\=\dfrac{2 \pi}{3}$$
