Answer
$$\dfrac{9 \pi }{2}$$
Work Step by Step
Consider the shell model to compute the volume:
$$V=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\= \int_0^{\sqrt 3} (2 \pi) \cdot (y)[3-(3-y^2) dy \\=2 \pi \times \int_0^{\sqrt 3} y^3 dy \\=2\pi \times [\dfrac{y^4}{4}]_0^{\sqrt 3} \\=\dfrac{9 \pi }{2}$$