4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{101ec3c2-699e-4c74-bfdc-d8c610646571-05_504_844_255_543}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The curve \(C\) with equation \(y = \frac { 2 } { ( 4 + 3 x ) } , x > - \frac { 4 } { 3 }\) is shown in Figure 1
The region bounded by the curve, the \(x\)-axis and the lines \(x = - 1\) and \(x = \frac { 2 } { 3 }\), is shown shaded in Figure 1
This region is rotated through 360 degrees about the \(x\)-axis.
- Use calculus to find the exact value of the volume of the solid generated.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{101ec3c2-699e-4c74-bfdc-d8c610646571-05_583_433_1398_753}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a candle with axis of symmetry \(A B\) where \(A B = 15 \mathrm {~cm}\). \(A\) is a point at the centre of the top surface of the candle and \(B\) is a point at the centre of the base of the candle. The candle is geometrically similar to the solid generated in part (a). - Find the volume of this candle.