A solid ice cube in the shape of a perfect cube has edge length centimeters

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A solid ice cube in the shape of a perfect cube has edge length

x

centimeters. As the cube melts, the edge length decreases at a constant rate of

0.05\text{ cm/min}

. The volume

V

(in

\text{cm}^3

) of a cube with edge length

x

V = x^{3}

. (a) Calculate the instantaneous rate at which the volume of the ice cube is changing when the edge length is

4\text{ cm}

. Include units in your answer. (b) For what edge length will the volume be decreasing at exactly

10\text{ cm}^3\text{/min}

? Justify your answer algebraically.