\includegraphics{figure_2}

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.

\begin{enumerate}[label=(\alph*)]
\item Write down the $y$-coordinates of $A$ and $B$. [1]

\item Show that an equation of $C$ is $\frac{3y + 4}{y} = 0$, $y \neq 0$. [1]
\end{enumerate}

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 $360°$ about the $y$-axis to form a solid shape $S$.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the volume of $S$, giving your answer in the form $\pi (a + b \ln c)$, where $a$, $b$ and $c$ are integers. [7]
\end{enumerate}

The solid shape $S$ is used to model a cooling tower. Given that 1 unit on each axis represents 3 metres,

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item show that the volume of the tower is approximately $15\,500$ m$^3$. [2]
\end{enumerate}

\hfill \mbox{\textit{Edexcel C4  Q17 [11]}}