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.
717 exam-style questions on Edexcel A Level Maths Differentiation, 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. Each one has a worked solution and a mark scheme showing where the marks go.