A solid sphere is dissolving in a chemical solution. The surface area of the sphere, AAA, is decreasing at a constant rate.
Show that the rate of decrease of the radius, rrr, of the sphere is inversely proportional to rrr.
You may use the following formula for the surface area of a sphere:
A=4πr2 A = 4\pi r^2 A=4πr2Practise 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.
