Level 3 Differentiation Walkthrough

Question 3(c)

2022 Paper - Related rates for a bowl of water

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Question

When the height of the water level in the bowl is \(h\) cm, the volume, \(V\) cm\(^3\), of water in the bowl is given by

\[ V=\pi\left(\frac{3}{2}h^2+3h\right). \]

Water is poured into the bowl at a constant rate of \(20\text{ cm}^3\text{ s}^{-1}\).

Find the rate, in \(\text{cm s}^{-1}\), at which the height of the water level is increasing when \(h=3\text{ cm}\).

You must use calculus and show any derivatives that you need when solving this problem.

Try the question yourself first. If you get stuck, open the hints before using the full walkthrough.