2022 THREE(c)

The diagram below shows the cross-section of a bowl containing water.

When the height of the water level in the bowl is $h$ cm, the volume, $V$ cm${}^3$, of water in the bowl is
given by $V=\pi \left(\frac{3}{2}{h}^2+3h\right)$.

Water is poured into the bowl at a constant rate of $20$ cm${}^3$ s${}^{-1}$.

Find the rate, in cm s${}^{-1}$, at which the height of the water level is increasing when the height of the
water level is $3$ cm.

*You must use calculus and show any derivatives that you need to find when solving this problem.*