3
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9cdb00a6-1e86-4185-bb73-ed3ecab981ba-2_369_863_799_296}
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\caption{Fig. 1}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9cdb00a6-1e86-4185-bb73-ed3ecab981ba-2_225_652_943_1192}
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\caption{Fig. 2}
\end{figure}
Fig. 1 shows an open tank in the shape of a triangular prism. The vertical ends \(A B E\) and \(D C F\) are identical isosceles triangles. Angle \(A B E =\) angle \(B A E = 30 ^ { \circ }\). The length of \(A D\) is 40 cm . The tank is fixed in position with the open top \(A B C D\) horizontal. Water is poured into the tank at a constant rate of \(200 \mathrm {~cm} ^ { 3 } \mathrm {~s} ^ { - 1 }\). The depth of water, \(t\) seconds after filling starts, is \(h \mathrm {~cm}\) (see Fig. 2).
- Show that, when the depth of water in the tank is \(h \mathrm {~cm}\), the volume, \(V \mathrm {~cm} ^ { 3 }\), of water in the tank is given by \(V = ( 40 \sqrt { } 3 ) h ^ { 2 }\).
- Find the rate at which \(h\) is increasing when \(h = 5\).