The volume of a cube with sides of length s is given by .Find the rate of change of volume with respect to centimeters.
A)648
B)216
C)36
D)108
E)72

Question

The volume of a cube with sides of length s is given by  .Find the rate of change of volume with respect to  centimeters.
A)648 
B)216 
C)36 
D)108 
E)72

Quizplus · Accepted Answer

The volume of a cube with sides of length s is given by: 
V = s^3

We want to find the rate of change of volume with respect to s. 
That is, we want to find dV/ds.

Using the power rule of differentiation, we have: 
dV/ds = 3s^2

At the given length of 9 cm, we have: 
dV/ds = 3(9)^2 = 243

Therefore, the best choice is D) 108 cm^3/cm.

The Volume of a Cube with Sides of Length S