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Denote the original area by A, denote the new area by A', denote the original circumference by C, and denote the new circumference by C'. C=2*pi*r so C'=2C=2*pi*(2r). So doubling the circumference corresponds to doubling the radius. A=pi*r2. A'/A=pi*(2r)2/[pi*r2]=4. So doubling the radius quadruples the area.

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Q: What happens to the area if the circumference of a circle is doubled?
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