8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c9758792-ca4c-4837-bd7c-e695fe0c0cdf-12_662_719_127_609}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A cuboid has a rectangular cross-section where the length of the rectangle is equal to twice its width, \(x \mathrm {~cm}\), as shown in Figure 2.
The volume of the cuboid is 81 cubic centimetres.
- Show that the total length, \(L \mathrm {~cm}\), of the twelve edges of the cuboid is given by
$$L = 12 x + \frac { 162 } { x ^ { 2 } }$$
- Use calculus to find the minimum value of \(L\).
- Justify, by further differentiation, that the value of \(L\) that you have found is a minimum.