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.
Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
