17.
Figure 2
\includegraphics[max width=\textwidth, alt={}, center]{615ec68b-3a32-4309-bb54-acf39ed09f96-12_674_776_330_541}
Figure 2 shows a sketch of the curve \(C\) with equation \(y = \frac { 4 } { x - 3 } , x \neq 3\).
The points \(A\) and \(B\) on the curve have \(x\)-coordinates 3.25 and 5 respectively.
- Write down the \(y\)-coordinates of \(A\) and \(B\).
- Show that an equation of \(C\) is \(\frac { 3 y + 4 } { y } , y \neq 0\).
(1)
The shaded region \(R\) is bounded by \(C\), the \(y\)-axis and the lines through \(A\) and \(B\) parallel to the \(x\)-axis. The region \(R\) is rotated through \(360 ^ { \circ }\) about the \(y\)-axis to form a solid shape \(S\). - Find the volume of \(S\), giving your answer in the form \(\pi ( a + b \ln c )\), where \(a , b\) and \(c\) are integers.
The solid shape \(S\) is used to model a cooling tower. Given that 1 unit on each axis represents 3 metres,
- show that the volume of the tower is approximately \(15500 \mathrm {~m} ^ { 3 }\).