The volume of a cube is increasing at a rate of 300 cm3/min at the instant when the edge is 20 cm. Find the rate at which the edge is changing.

Question

The volume of a cube is increasing at a rate of 300 cm3/min at the instant when the edge is 20 cm. Find the rate at which the edge is changing.

Answer 1

Let x = length of an edge of the cube at time t

 

     V = volume of the cube at time t

 

Given:  dV/dt = 300

 

Find:  dx/dt when x = 20

 

Solution:  V = x³

 

            Differentiate implicitly with respect to t to get

 

                  dV/dt = 3x²(dx/dt)

 

                  So, 300 = 3(20)²(dx/dt)

 

                  dx/dt = 0.25 cm/min