4 Fig. 4 is a diagram of a garden pond.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{72de4365-c3f0-4106-8daf-3047afeab723-3_296_746_351_657}
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\caption{Fig. 4}
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The volume \(V \mathrm {~m} ^ { 3 }\) of water in the pond when the depth is \(h\) metres is given by
$$V = \frac { 1 } { 3 } \pi h ^ { 2 } ( 3 - h )$$
- Find \(\frac { \mathrm { d } V } { \mathrm {~d} h }\).
Water is poured into the pond at the rate of \(0.02 \mathrm {~m} ^ { 3 }\) per minute.
- Find the value of \(\frac { \mathrm { d } h } { \mathrm {~d} t }\) when \(h = 0.4\).