Question

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

Answer 1

Answer:

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

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