How fast is the edge length of a cube increasing?...

Question

How fast is the edge length of a cube increasing when the volume of the cube is increasing at a rate of 144cm^3/s and the edge length is 4cm?

Answer 1

The edge length (s) is related to the volume (V) of the cube by the relation V = s³.

 

Taking the derivative with respect to time, dV/dt = 3s² ds/dt by the chain rule.

 

We want to know how fast the edge is increasing when the volume is changing at the rate of 144 cm³/s and the edge length is 4 cm, so solve for ds/dt and substitute.

 

Good luck!