The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the diameter is 40mm? Note: The volume of a sphere of radius, r, is given by V = (4/3)pi r^3

The volume is increasing at a rate of 25,133 mm/s.

Step-by-step explanation:

Diameter is 40mm

Radius is half the diameter, so

How fast is the volume increasing when the diameter is 40mm?

We have to apply implicit differentiation, of V and r in function of t. So

The radius of a sphere is increasing at a rate of 5 mm/s.

This means that

Then

The volume is increasing at a rate of 25,133 mm/s.

true? is that what you're asking or do you mean something else?