Answer
$$\dfrac{2 \pi \space R^3}{3}$$
Work Step by Step
We know that the area of the cross-section of the hemisphere is given as follows: $$Area=R^2\pi- h^2 \pi=\pi (R^2-h^2)$$
Now, we will integrate the integral to calculate the volume as follows:
$$Volume = V_{\space cylinder}-V_{\space Cone} \\=\pi R^2- \dfrac{ \pi R^2}{3} (R) \\=\dfrac{2 \pi \space R^3}{3}$$
