A spherical balloon is being inflated with helium at a rate of 20π cm3/min. How fast is the balloon's radius changing when the radius is 1 cm?

Using implicit differentiation, it is found that the radius is changing at a rate of 5 cm/min.

The volume of a sphere of radius r is given by:

Applying implicit differentiation, the rate of change is of:

Then:

The radius is changing at a rate of 5 cm/min.

A similar problem is given at link

5 cm/min

Step-by-step explanation:

A spherical balloon is being inflated with helium at a rate of 20π cm³/min.

The volume of a sphere is given by :

...(1)

Differentiate equation (1) wrt t as follows :

Put dV/dt = 20π cm³/min and r = 1 cm, we can fin dr/dt

So, the radius of changing at the rate of 5 cm/min.