Answer
$$8 \pi$$
Work Step by Step
Consider the shell model to compute the volume:
$$V=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\= \int_0^{2} (2 \pi) (x) \times [x-\dfrac{(-x)}{2}] dx \\ = \int_{0}^{2} [2 \pi x^2] dx \\ =\pi \times [x^3]_{0}^{2}\\=8 \pi$$
