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≤20 V = \frac{1}{5}h^2(h + 15) \quad 0 \le h \le 20 V=51h2(h+15)0≤h≤20The 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 Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, 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.
