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Using implicit differentiation, and considering that the inflation rate is of 200 cubic feet per minute and the radius is of 5 feet, it is found that:
- The radius is increasing at a rate of 0.6366 feet per minute.
- The surface area is changing at a rate of 80 feet squared per minute.
The volume of an <u>sphere of radius r</u> is given by:
Applying <em>implicit differentiation</em>, the rate of change is given by:
For this problem:
- Inflation rate of 200 cubic feet per minute, hence
- Radius is of 5 feet, hence
Then:
The radius is increasing at a rate of 0.6366 feet per minute.
The surface area is:
Hence, the <em>rate of change</em> is:
Hence:
The surface area is changing at a rate of 80 feet squared per minute.
A similar problem is given at brainly.com/question/9543179