9.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{582cda45-80fc-43a8-90e6-1cae08cb1534-15_831_1167_118_513}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}

Figure 4 shows a plan view of a sheep enclosure.\\
The enclosure $A B C D E A$, as shown in Figure 4, consists of a rectangle $B C D E$ joined to an equilateral triangle $B F A$ and a sector $F E A$ of a circle with radius $x$ metres and centre $F$.

The points $B , F$ and $E$ lie on a straight line with $F E = x$ metres and $10 \leqslant x \leqslant 25$
\begin{enumerate}[label=(\alph*)]
\item Find, in $\mathrm { m } ^ { 2 }$, the exact area of the sector $F E A$, giving your answer in terms of $x$, in its simplest form.

Given that $B C = y$ metres, where $y > 0$, and the area of the enclosure is $1000 \mathrm {~m} ^ { 2 }$,
\item show that

$$y = \frac { 500 } { x } - \frac { x } { 24 } ( 4 \pi + 3 \sqrt { 3 } )$$
\item Hence show that the perimeter $P$ metres of the enclosure is given by

$$P = \frac { 1000 } { x } + \frac { x } { 12 } ( 4 \pi + 36 - 3 \sqrt { 3 } )$$
\item Use calculus to find the minimum value of $P$, giving your answer to the nearest metre.
\item Justify, by further differentiation, that the value of $P$ you have found is a minimum.
\end{enumerate}

\hfill \mbox{\textit{Edexcel C2 2016 Q9 [15]}}