4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b85f4635-aa93-4c6a-9d1f-2ef5bac1b48c-03_725_560_310_571}
\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 \(2 x \mathrm {~cm}\) by \(x \mathrm {~cm}\) 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
$$A = 4 x ^ { 2 } + \frac { 3090 } { x } .$$