A specialized coolant storage tank has a depth of 20 cm20\text{ cm}20 cm. The tank is initially empty and a liquid refrigerant is pumped into it. When the depth of the refrigerant is h cmh\text{ cm}h cm, the volume of the liquid in the tank, V cm3V\text{ cm}^3V cm3, is modelled by the equation V=15h2(h+15)0≤h≤20V = \frac{1}{5}h^2(h + 15) \quad 0 \le h \le 20V=51h2(h+15)0≤h≤20 The refrigerant is pumped into the tank at a constant rate of 350 cm3 s−1350\text{ cm}^3\text{ s}^{-1}350 cm3 s−1. According to the model:
calculate the time taken to fill the tank to its maximum depth.
determine the rate of change of the depth of the liquid, in cm s−1\text{cm s}^{-1}cm s−1, at the instant when h=10h = 10h=10.
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.