4. (1+3 = 4 marks) (a) If A is the area of a circle of radius r and the circle expands as time passes, find dA/dt in terms of dr/dt. (b) Suppose oil spills from a ruptured tanker ship and spreads across the surface of the sea in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 metre/second, how fast is the area of the spill increasing when the radius is 30 metres?

Fig: 1