A spherical snowball melts in such a way that its radius decreases at a constant rate…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A spherical snowball melts in such a way that its radius decreases at a constant rate of 0.20 cm min⁻¹. When the radius reaches 15 cm, the temperature and external conditions remain steady.
(a) Compute the instantaneous rate at which the snowball’s volume is changing when the radius is 15 cm. Include sign and units.
(b) Compute the instantaneous rate at which the snowball’s surface area is changing at the same moment. Include sign and units.
(c) Which quantity—volume or surface area—is decreasing more rapidly in absolute value at that instant? Support your answer with calculations and a brief explanation.