Blowing Soap Bubbles Carlos is blowing air into a spherical soap bubble at the rate of 10 cm3/sec. How fast is the radius of the bubble changing when the radius is 11 cm? (Round your answer to four decimal places.)

The rate of change of the radius is 0.0066 cm/s when the radius is 11 cm.

Step-by-step explanation:

The change in volume is according to the inflow of air, that has a rate of 10 cm3/s.

The volume of the sphere can be defined as:

To calculate the rate of change of the radius (dr/dt), we have to derive the last expression.

Then we have an expression for dr/dt:

For r = 11 cm, we have:

The rate of change of the radius is 0.0066 cm/s when the radius is 11 cm.