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=34πr3717 exam-style questions on Edexcel A Level Maths Differentiation, 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. Each one has a worked solution and a mark scheme showing where the marks go.