6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3cf64017-e982-4165-9885-8524aaabdf84-10_456_553_264_571}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a vertical cross-section of a vase.
The inside of the vase is in the shape of a right-circular cone with the angle between the sides in the cross-section being \(60 ^ { \circ }\). When the depth of water in the vase is \(h \mathrm {~cm}\), the volume of water in the vase is \(V \mathrm {~cm} ^ { 3 }\).
- Show that \(V = \frac { 1 } { 9 } \pi h ^ { 3 }\).
The vase is initially empty and water is poured in at a constant rate of \(120 \mathrm {~cm} ^ { 3 } \mathrm {~s} ^ { - 1 }\).
- Find, to 2 decimal places, the rate at which \(h\) is increasing
- when \(h = 6\),
- after water has been poured in for 8 seconds.
6. continued