A spherical weather balloon is leaking helium. The volume, VVV, of the balloon is decreasing at a constant rate.
Show that the rate of decrease of the radius, rrr, of the balloon is inversely proportional to r2r^2r2.
You may use the following formula for the volume of a sphere:
V=43πr3 V = \frac{4}{3}\pi r^3 V=34πr3Practise 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.
