6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{66abdef1-072e-41eb-a933-dd51a96330ff-14_488_1511_246_278}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
A river is being studied.
At one particular place, the river is 15 m wide.
The depth, \(y\) metres, of the river is measured at a point \(x\) metres from one side of the river.
Figure 1 shows a plot of the cross-section of the river and the coordinate values \(( x , y )\)
- Use the trapezium rule with all the \(y\) values given in Figure 1 to estimate the cross-sectional area of the river.
The water in the river is modelled as flowing at a constant speed of \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) across the whole of the cross-section.
- Use the model and the answer to part (a) to estimate the volume of water flowing through this section of the river each minute, giving your answer in \(\mathrm { m } ^ { 3 }\) to 2 significant figures.
Assuming the model,
- state, giving a reason for your answer, whether your answer for part (b) is an overestimate or an underestimate of the true volume of water flowing through this section of the river each minute.