C.MM.1.2
Create mathematical models to explain phenomena that exist in the natural sciences, social sciences, liberal arts, fine and performing arts, and/or humanities contexts.
Example Problems
The radius of a sphere is decreasing at a rate of 2 feet per minute. At a certain instant, the radius is 15 feet.
What is the rate of change of the volume of the sphere at that instant (in cubic feet per minute)?
What is the rate of change of the volume of the sphere at that instant (in cubic feet per minute)?
The radius of a sphere is increasing at a rate of 0.25 meters per hour. At a certain instant, the radius is 6 meters.
What is the rate of change of the volume of the sphere at that instant (in cubic meters per hour)?
What is the rate of change of the volume of the sphere at that instant (in cubic meters per hour)?
The radius of a sphere is increasing at a rate of 5 kilometers per day. At a certain instant, the radius is 2 kilometers.
What is the rate of change of the volume of the sphere at that instant (in cubic kilometers per day)?
What is the rate of change of the volume of the sphere at that instant (in cubic kilometers per day)?

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