A cube of soft clay expands uniformly as it is heated
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A cube of soft clay expands uniformly as it is heated. Let s denote the length of an edge (in centimeters), and let V denote the volume (in cubic centimeters). At the instant when V=125000 cm3 the volume is increasing at a rate of 150 cm3 s−1. The volume of a cube of edge length s is V=s3.
(a) Determine the rate at which the edge length s is increasing, in centimeters per second, at the specified instant.
(b) Assuming the rate you found in part (a) remains constant, estimate (to three significant figures) how many seconds it will take for the edge length to grow from 50 cm to 55 cm. Show your reasoning clearly.