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Question

How do you write the area a of a circle as a function of its circumference?


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Solution

Finding the relation between area and circumference by using the formula:

Let the area of circle be A and circumference C.

Formula for the area of circle is given by (πr2) where r is the radius of the circle.

and the circumference is given by 2πr.

Where π is a constant and r is the radius of the circle.

C=2(π)r

C2=22(π)2r2 (Squaring both sides)

C2=4(π)(π)r2

C2=4(π)A A=πr2

A=C24(π)

Therefore, area as a function of the circumference is given by A=C24(π).


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