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 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.
