15.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{48f9a252-61a2-491d-94d0-8470aee96942-22_750_1100_276_541}
\captionsetup{labelformat=empty}
\caption{Figure 7}
\end{center}
\end{figure}

Figure 7 shows an open tank for storing water, $A B C D E F$. The sides $A C D F$ and $A B E F$ are rectangles. The faces $A B C$ and $F E D$ are sectors of a circle with radius $A B$ and $F E$ respectively.

\begin{itemize}
  \item $A B = F E = r \mathrm {~cm}$
  \item $A F = B E = C D = l \mathrm {~cm}$
  \item angle $B A C =$ angle $E F D = 0.9$ radians
\end{itemize}

Given that the volume of the tank is $360 \mathrm {~cm} ^ { 3 }$\\
a. show that the surface area of the tank, $S \mathrm {~cm} ^ { 2 }$, is given by

$$S = 0.9 r ^ { 2 } + \frac { 1600 } { r }$$

(4)

Given that $r$ can vary\\
b. use calculus to find the value of $r$ for which $S$ is stationary.\\
c. Find, to 3 significant figures the minimum value of $S$.\\

\hfill \mbox{\textit{Edexcel PMT Mocks  Q15 [10]}}