A solid cylindrical ice pillar is melting in the ocean. At time t t\,t hours, the pillar has radius R R\,R metres and height H H\,H metres. The height is maintained such that H=8RH = 8RH=8R throughout the melting process.
The area of the pillar's circular top face, SSS, is decreasing at a constant rate of 1.5 m2 h-1.
Determine the value of dRdt\displaystyle \frac{dR}{dt}dtdR at the instant when R=4R = 4R=4.
Determine the rate of decrease of the volume of the ice pillar at the instant 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.