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Problem

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Textbook Expert
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28 Oct 2021

Given information

Given to show that the rate of change of the area of a circle with respect to its radius (at any ) is equal to the circumference of the circle. Also, explain it graphically and describe a method to detail the change in the area when the change in radius is smaill.

Step-by-step explanation

Step 1.

Use the formula of the area of a circle to explain the first part of the question.

 

Finding the derivative of the rate of change so, differentiate the area with respect to time

   

Thus,  is the circumference of the circle.

Hence, it is verified that the rate of change of the area of a circle with respect to its radius (at any ) is equal to the circumference of the circle.

 

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