Edexcel P4 2022 June — Question 3

Exam BoardEdexcel
ModuleP4 (Pure Mathematics 4)
Year2022
SessionJune
TopicConnected Rates of Change

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 \(0.5 \mathrm {~mm} ^ { 2 } \mathrm {~s} ^ { - 1 }\)
  1. Find \(\frac { \mathrm { d } x } { \mathrm {~d} t }\) when \(x = 7\)
  2. Find, according to the model, the rate of decrease of the volume of the tablet when \(x = 4\)