- In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ab572f1e-2828-4ab3-b148-605f35ccd1db-14_385_526_447_420}
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\caption{Figure 1}
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\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ab572f1e-2828-4ab3-b148-605f35ccd1db-14_485_433_388_1187}
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\caption{Figure 2}
\end{figure}
A large pile of concrete waste is created on a building site.
Figure 1 shows a central vertical cross-section of the concrete waste.
The curve \(C\), shown in Figure 2, has equation
$$y + x ^ { 2 } = 2 \quad 0 \leqslant x \leqslant \sqrt { 2 }$$
The region \(R\), shown shaded in Figure 2, is bounded by the \(y\)-axis, the \(x\)-axis and the curve \(C\).
The volume of concrete waste is modelled by the volume of revolution formed when \(R\) is rotated through \(360 ^ { \circ }\) about the \(y\)-axis. The units are metres.
The density of the concrete waste is \(900 \mathrm { kgm } ^ { - 3 }\)
- Use the model to estimate the mass of the concrete waste. Give your answer to 2 significant figures.
- Give a limitation of the model.
The mass of the concrete waste is approximately 5500 kg .
- Use this information and your answer to part (a) to evaluate the model, giving a reason for your answer.