| Exam Board | CAIE |
| Module | P1 (Pure Mathematics 1) |
| Year | 2012 |
| Session | June |
| Topic | Differential equations |
4 A watermelon is assumed to be spherical in shape while it is growing. Its mass, \(M \mathrm {~kg}\), and radius, \(r \mathrm {~cm}\), are related by the formula \(M = k r ^ { 3 }\), where \(k\) is a constant. It is also assumed that the radius is increasing at a constant rate of 0.1 centimetres per day. On a particular day the radius is 10 cm and the mass is 3.2 kg . Find the value of \(k\) and the rate at which the mass is increasing on this day.