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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)?

Respuesta :

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

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