Calculus problem

Question

The radius of a circular oil spill on the surface of the ocean is growing a rate of 2 cm / s. Determine the rate at which area is being consumed by the oil spill when a) r = 10 cm, and later when b) r = 1000 cm. Round to two decimal places.

Answer 1

Use the formula

 

dA/dt = (dA/dr) * (dr/dt)

 

dA/dr is the derivarive of area with respect to radius

dr/dt is the rate at which the radius changes