A circular oil slick on the surface of a calm lake is expanding uniformly
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A circular oil slick on the surface of a calm lake is expanding uniformly. At the instant when the radius of the slick is 10 m, the radius is increasing at a rate of 0.25 m/min.
(a) Calculate the instantaneous rate of change of the area of the slick at that instant. Express your answer in square meters per minute.
(b) Determine the instantaneous rate of change of the circumference of the slick at the same instant. Give appropriate units.
(c) Interpret the result from part (a) in the context of the physical situation. What does the sign and magnitude of your answer tell you about the oil slick?