Question

Given that the volume decreases at a rate of 3 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 64 cubic meters

Answer 1

V=L³
L= ³√V or V^⅓
dL/dV= ⅓V ^(⅓-1) = ⅓V^-⅔

dV/dt= -3m³M-¹

dL/dt= dV/dt • dL/dV
dL/dt = -3 • ⅓V^-⅔
dL/dt = -V^-⅔
dL/dt = -(64)^-⅔
dL/dt = - (4)-²
= -1/16 mM-¹