Answer
$\dfrac{9 \pi }{2}$
Work Step by Step
We need to use the shell model as follows:
$V=\int_p^{q} (2 \pi) \cdot (\space radius \space of \space shell) ( height \space of \space Shell) \space dy$
$ \implies V= \int_0^{\sqrt 3} (2 \pi) \cdot (y)[3-(3-y^2) dy=2 \pi \times \int_0^{\sqrt 3} y^3 dy$
or, $=2\pi \times [\dfrac{y^4}{4}]_0^{\sqrt 3}$
or, $=\dfrac{9 \pi }{2}$
