A tanker is spilling oil into the water resulting in an oil slick that is close to circular. At te time that the slick's diameter is growing at a rate of 8 ft/sec, the diameter is 250 feet. At what rate is the area of the oil sick increasing?

Answer 1

area = A = pi r^2
dA/dr = 2 pi r
dA/dt = 2 pi r dr/dt
which we did not really have to do because obviously the rate of change of area is the rate of change of radius times the circumference.