A solid block of ice is a perfect cube with edge length

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

Problem

5.0\text{ cm}

. The ice is melting uniformly so that its mass decreases at a constant rate of

10.0\text{ g\,min}^{-1}

. The density of ice is

0.92\text{ g\,cm}^{-3}

. Let

s

be the edge length (in centimeters) and

V

the volume (in cubic centimeters) of the cube. Recall that

V=s^{3}

. (a) Compute the rate at which the *volume* of the cube is changing, in cubic centimeters per minute, at the given instant. (b) Determine the rate at which the *edge length*

s

is changing, in centimeters per minute, at this instant. Specify the sign of your answer and explain its significance. (c) If the magnitude of the edge–length rate found in part (b) were to remain constant for the rest of the melting process, estimate the additional time required (in minutes) for the cube to melt completely. State any assumptions you make.

Related theory

Browse the problem library