A grain hopper dispenses wheat at a constant rate of 12 cm3s-1 onto a level floor, where it forms a conical pile. After t t\,t seconds, the pile has a height of h cmh\text{ cm}h cm and a volume of V cm3V\text{ cm}^3V cm3. The volume is modeled by the equation:
V=πh312V = \frac{\pi h^3}{12}V=12πh3
Show that when t=6t = 6t=6,
dVdh=916π3\frac{dV}{dh} = 9 \sqrt[3]{16\pi}dhdV=9316π
Hence, find the rate at which the height of the pile is increasing when t=6t = 6t=6. Give your answer in cm s−1\text{cm s}^{-1}cm s−1 to three significant figures.
Practise Edexcel A Level Maths 9.10 Rates of Change with exam-style questions for A Level Maths. 24 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.