Question

The volume of a cube decreases at a rate of 0.3 ft3/min. What is the rate of change of the side length when the side lengths are 9 ft?

Answer 1

Explanation:

side = 9 ft

the volume of a cube is

V = side³

if V decreases by a to V', then each side decreases by side - cubic root of V'.

V = 9³ = 729 ft³

V' = (729 - 0.3) ft³ = 728.7 ft³

side' = cubic root (728.7) = 8.998765263... ft

difference side - side' = 0.001234737... ft

so, the change rate at 9 ft is

0.001234737... ft/min.