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=4πr2717 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.