Answer
$$\dfrac{8 \pi}{3}$$
Work Step by Step
Consider the shell model to compute the volume:
$$Volume=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\= \int_{0}^{2} (2 \pi) \cdot y (2y-y^2) dy \\ =2 \pi (\dfrac{2y^3}{3}-\dfrac{y^4}{4})_{0}^{2} \\= [\dfrac{16(2 \pi) }{3}-4(2 \pi)] \\=\dfrac{8 \pi}{3}$$
