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Take the formulas for the area and circumference of a circle, and massage them.

R = radius = 1/2 of the diameter

A = Area of a circle = pi R2 = pi (D/2)2 = pi D2/4

C = Circumference of a circle = (pi D) or (2 pi R)

C = 2 pi R = 2 (pi R2)/R

(R) C = 2 A

(C/2pi) C = 2 A

C2 / 2pi = 2 A

C2 = 4 pi A

C = sqrt ( 4 pi A ) or 2 sqrt ( pi A )

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Q: How do you find the circumference of a circle as a function of its area?
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