Edexcel C4 2008 June — Question 3

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
Year2008
SessionJune
TopicNon-constant acceleration

3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{fb1924cc-9fa3-4fde-ba4d-6fb095f7f70b-04_444_705_205_623} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a right circular cylindrical metal rod which is expanding as it is heated. After \(t\) seconds the radius of the rod is \(x \mathrm {~cm}\) and the length of the rod is \(5 x \mathrm {~cm}\). The cross-sectional area of the rod is increasing at the constant rate of \(0.032 \mathrm {~cm} ^ { 2 } \mathrm {~s} ^ { - 1 }\).
  1. Find \(\frac { \mathrm { d } x } { \mathrm {~d} t }\) when the radius of the rod is 2 cm , giving your answer to 3 significant figures.
  2. Find the rate of increase of the volume of the rod when \(x = 2\).
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