$20$a$.[3$ marks$]$

The vertical cross$-$section of a container is shown in the following diagram.

The curved sides of the cross$-$section are given by the equation $y=0\mathrm{.}25x^2-16.$ The horizontal crosssections are circular. The depth of the container is $48cm.$

If the container is filled with water to a depth of $hcm,$ show that the volume, $Vc{m}^3,$ of the water is given by $V=4(\frac{h^2}{2}+16h)$