Question

The side of a cube is decreasing at a rate of 9 millimeters per minute.

At a certain instant, the side is 19 millimeters.
What is the rate of change of the volume of the cube at that instant (in cubic millimeters per minute)?

Answer 1

the rate of change of the volume of the cube is -9747 cubic millimeters per minute

Step-by-step explanation:

The computation of the rate of change of the volume of the cube is given below:

As we know that

The volume of the cube is x^3

Now differentiate it with time t

So

dV÷ dt = 3x^2 dx ÷ dt

Now put the values

= 3(19)^2 (-9)

= -9747 cubic millimeters per minute

hence, the rate of change of the volume of the cube is -9747 cubic millimeters per minute