An offshore oil leak spreads a thin circular film of oil on the ocean surface
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
An offshore oil leak spreads a thin circular film of oil on the ocean surface. At noon the film has radius 5 m, and the area of the film is increasing at a rate of 20 m2 per minute.
(a) Write an equation that relates the area A of the circular film to its radius r. Clearly define each variable, including units.
(b) Using your relationship from part (a), determine the instantaneous rate of change of the radius, dr/dt, at noon. State your answer with appropriate units and explain each step of your calculation.