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. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, 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.
