OCR MEI C3 2013 June — Question 4

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Year2013
SessionJune
TopicNon-constant acceleration

4 Water flows into a bowl at a constant rate of \(10 \mathrm {~cm} ^ { 3 } \mathrm {~s} ^ { - 1 }\) (see Fig. 4). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{28ce1bcc-e9d5-4ae6-98c0-67b5b8c50bc6-3_422_385_1628_815} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure} When the depth of water in the bowl is \(h \mathrm {~cm}\), the volume of water is \(V \mathrm {~cm} ^ { 3 }\), where \(V = \pi h ^ { 2 }\). Find the rate at which the depth is increasing at the instant in time when the depth is 5 cm .