Answer
$$\dfrac{\pi r^2 h}{3}$$
Work Step by Step
Consider the shell model to compute the volume:
$$Volume=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\=(2 \pi) \int_{0}^{r}[h-\dfrac{h x}{r}] dx \\=(2 \pi) \int_{0}^{r}[h \space x-\dfrac{hx^2}{r}] dx \\=\dfrac{\pi \space r^2 h}{3}$$