The radius of a sphere increases at a constant rate of 2 com/min at the time when the volume of the sphere is 40 cm^3ç what is the rate of increase of the volume in cm^3/min?

Step-by-step explanation:

The volume of a sphere is:

(1)

We know that:

If we take the derivative of (1) with respect of time t, we ca n find the rate of increase of the volume.

(2)

We also know that the volume is 40 cm³, then using the (1) we can get the radius at this value.

Solving (1) for r, we have:

Finally dV/dt will be:

I hope it helps you!