A cube of side length centimeters is uniformly coated with a dissolving chemical so…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A cube of side length s centimeters is uniformly coated with a dissolving chemical so that the side length is decreasing at a constant rate of 0.10 cm/s.
(a) Derive a formula for the instantaneous rate of change of the cube’s volume V in terms of s.
(b) Compute dV/dt when s=2 cm and when s=1 cm, giving units in each case.
(c) Based on your results in part (b), describe whether the volume is decreasing at a constant rate or whether the magnitude of the rate changes over time. Provide a clear explanation that references the mathematical relationship between V and s.