All edges of a cube are expanding at a rate of 9 centimeters per second.How fast is the volume changing when each edge is 2 centimeters?
A)486
B)72
C)36
D)108
E)162

Question

All edges of a cube are expanding at a rate of 9 centimeters per second.How fast is the volume changing when each edge is 2 centimeters? ​
A)486 
B)72 
C)36 
D)108 
E)162

Quizplus · Accepted Answer

The volume of a cube is given by V = s³, where s is the length of one edge.
We can use the chain rule to find the rate of change of volume with respect to time:

dV/dt = dV/ds * ds/dt

The first derivative can be found using the power rule:

dV/ds = 3s²

And we are given that ds/dt = 9 cm/s.
Substituting s = 2 cm, we have:

dV/dt = (3(2)²)(9) = 108 cm³/s

Therefore, the volume is changing at a rate of 108 cm³/s when each edge is 2 centimeters. The answer is D.

All Edges of a Cube Are Expanding at a Rate