The volume of a spherical balloon is increasing at the constant rate of 8 cubic feet per minute. How fast is the radius incresing when the radius is exactly 10 feet? How fast is the surface area increasing at that time?

Rate of increase of radius = 0.0064 ft/sec

Rate of increase of surface area = 1.61

Step-by-step explanation:

Given that:

Rate of change of volume of a spherical balloon = 8 cubic feet per minute

Radius, = 10 feet

To find:

The rate of change of radius at this moment and rate of change of surface area at this moment?

Solution:

First of all, let us have a look at the formula:

Now, differentiating the volume and area, we get: