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