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 Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, matched to the Edexcel A Level Maths (9MA0) 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.
