Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1m/s, how fast is the area of the spill increasing when the radius is 30m?

Answer 1

Area = πr^2
d(area)/dt = 2πr dr/dt
but dr/dt = 1 m/s

d(area)/dt = 2π(30)(1) = 60π m^2/s