Answer
$$\dfrac{16 \pi (3\sqrt 2+5)}{15}$$
Work Step by Step
Consider the shell model to compute the volume:
$$Volume=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\=
\int_{0}^{2} (2 \pi) \cdot y (\sqrt y-(-y)) dy \\ =2 \pi \times [\dfrac{2y^2}{5}\sqrt y+\dfrac{y^2}{3}]_{0}^{2} \\=\dfrac{16 \pi (3\sqrt 2+5)}{15}$$
