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Using implicit differentiation, it is found that the rate of change of the surface area of the sphere -2201.293 square centimeters per second.
<h3>What is the volume of a sphere?</h3>- The volume of a sphere, of radius r, is given by:
- The surface area of a sphere, of radius r, is given by:
Applying <em>implicit differentiation</em>, the rate of change of both the volume and the surface area can be found, as follows:
Volume of 3131 cubic centimeters, hence:
The volume of a sphere is decreasing at a constant rate of 9988 cubic centimeters per minute, hence:
Then, the <u>rate of change of the surface area</u> of the sphere is given by:
The rate of change of the surface area of the sphere -2201.293 square centimeters per second.
To learn more about implicit differentiation, you can take a look at brainly.com/question/25608353