3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{960fe82f-c180-422c-b409-a5cdc5fae924-08_524_878_255_532}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A bowl with circular cross section and height 20 cm is shown in Figure 2.
The bowl is initially empty and water starts flowing into the bowl.
When the depth of water is \(h \mathrm {~cm}\), the volume of water in the bowl, \(V \mathrm {~cm} ^ { 3 }\), is modelled by the equation
$$V = \frac { 1 } { 3 } h ^ { 2 } ( h + 4 ) \quad 0 \leqslant h \leqslant 20$$
Given that the water flows into the bowl at a constant rate of \(160 \mathrm {~cm} ^ { 3 } \mathrm {~s} ^ { - 1 }\), find, according to the model,
- the time taken to fill the bowl,
- the rate of change of the depth of the water, in \(\mathrm { cm } \mathrm { s } ^ { - 1 }\), when \(h = 5\)