MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
For a melting ice cube, experimental observations suggest that the rate of decrease of volume is directly proportional to the square of its edge length, so that dtdV=−ka2, where k is a positive constant. At the instant when the edge length is 10cm, the volume is decreasing at 300cm3/s.
(i) Determine the constant of proportionality k (with units).
(ii) Using this value of k, find the rate at which the surface area of the cube is decreasing when the edge length is 8cm.
(iii) Comment on how the rate of decrease of surface area depends on the size of the cube, using your result.