3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2dffe245-b18a-4486-af8e-bad598ceb6e8-08_401_652_246_708}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
A tablet is dissolving in water.
The tablet is modelled as a cylinder, shown in Figure 1.
At \(t\) seconds after the tablet is dropped into the water, the radius of the tablet is \(x \mathrm {~mm}\) and the length of the tablet is \(3 x \mathrm {~mm}\).
The cross-sectional area of the tablet is decreasing at a constant rate of \(0.5 \mathrm {~mm} ^ { 2 } \mathrm {~s} ^ { - 1 }\)
- Find \(\frac { \mathrm { d } x } { \mathrm {~d} t }\) when \(x = 7\)
- Find, according to the model, the rate of decrease of the volume of the tablet when \(x = 4\)