A cylindrical ice pillar is melting in a laboratory. At time ttt minutes, the pillar has a radius r mmr\text{ mm}r mm and a length L=8r mmL = 8r\text{ mm}L=8r mm.
The cross-sectional area of the pillar, AAA, is decreasing at a constant rate of 1.2 mm2 min−11.2\text{ mm}^2\text{ min}^{-1}1.2 mm2 min−1.
Find the value of drdt\frac{dr}{dt}dtdr when r=3r = 3r=3.
Determine the rate of decrease of the volume of the pillar when r=5r = 5r=5.
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.
