Answer
$\dfrac{8 \pi}{3}$
Work Step by Step
We need to use the shell model as follows:
$V=\int_p^{q} (2 \pi) \cdot (\space radius \space of \space shell) ( height \space of \space Shell) \space dx$
$ \implies V= \int_{0}^{2} (2 \pi) \cdot y (2y-y^2) dy$
Now, $V=2 \pi (\dfrac{2y^3}{3}-\dfrac{y^4}{4})_{0}^{2}$
or, $=2 \pi \times (\dfrac{16}{3}-4)$
or, $=\dfrac{8 \pi}{3}$
