A spherical snowball is melting in the sun. The volume, VVV, of the snowball is decreasing at a constant rate.
Show that the rate of decrease of the snowball's surface area, AAA, is inversely proportional to its radius, rrr.
You may use the following formulae for a sphere:
V=43πr3andA=4πr2 V = \frac{4}{3}\pi r^3 \quad \text{and} \quad A = 4\pi r^2 V=34πr3andA=4πr2133 exam-style questions on WJEC A Level Maths 3.6.5 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.