10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4c08fbab-283e-4c92-89a4-10f68f37e133-16_319_508_237_719}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows a right circular cylindrical rod which is expanding as it is heated.
At time \(t\) seconds the radius of the rod is \(x \mathrm {~cm}\) and the length of the rod is \(6 x \mathrm {~cm}\).
Given that the cross-sectional area of the rod is increasing at a constant rate of \(\frac { \pi } { 20 } \mathrm {~cm} ^ { 2 } \mathrm {~s} ^ { - 1 }\), find the rate of increase of the volume of the rod when \(x = 2\)
Write your answer in the form \(k \pi \mathrm {~cm} ^ { 3 } \mathrm {~s} ^ { - 1 }\) where \(k\) is a rational number.