7. 7 A candlestick has base diamater 8 cm and height 28 cm , as shown in Figure 9. A model of the candlestick is shown in Figure 10, together with the equations that were used to create the model.
\begin{figure}[h]
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\caption{Figure 9}
\includegraphics[alt={},max width=\textwidth]{1b1cfccc-20f3-42f8-a1e1-d9405e7afcb9-16_835_428_456_276}
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\begin{figure}[h]
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\caption{Figure 10}
\includegraphics[alt={},max width=\textwidth]{1b1cfccc-20f3-42f8-a1e1-d9405e7afcb9-16_846_762_447_934}
\end{figure}
a Show that the volume generated by rotating the shaded region (in Figure 10) \(2 \pi\) radians about the \(y\)-axis is \(\frac { 112 } { 15 } \pi\)
b Hence find the volume of metal needed to create the candlestick.
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