Question

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 2.5 m/s. How fast is the area of the spill increasing when the radius is 14 m?

Answer 1

dr/dt = 2.5 m/s
r = 14 m
dA/dt - ?

Answer 2

dA/dt = d(pi*r^2)/dt = 2*pi*r*(dr/dt)

Answer 3

Plug in everything you have:
dA/dt = 2*pi*2.5*14 = 5*14pi = 70pi