8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{beec3800-227a-45a1-87b8-0ea96e0e6270-5_722_561_233_593}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{figure}
A manufacturer produces cartons for fruit juice. Each carton is in the shape of a closed cuboid with base dimensions 2 x cm by x cm and height \(h \mathrm {~cm}\), as shown in Fig. 4.
Given that the capacity of a carton has to be \(1030 \mathrm {~cm} ^ { 3 }\),
- express \(h\) in terms of \(x\),
- show that the surface area, \(A \mathrm {~cm} ^ { 2 }\), of a carton is given by
$$A = 4 x ^ { 2 } + \frac { 3090 } { x } .$$