To find the area of a circle given the circumference \( C = 4\pi \), we can use the formulas for circumference and area:
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The formula for the circumference of a circle is: \[ C = 2\pi r \] where \( r \) is the radius.
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We can set the given circumference equal to the formula: \[ 4\pi = 2\pi r \]
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To find the radius \( r \), we can divide both sides by \( 2\pi \): \[ r = \frac{4\pi}{2\pi} = 2 \]
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Now, we can find the area \( A \) of the circle using the area formula: \[ A = \pi r^2 \]
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Substitute \( r = 2 \) into the area formula: \[ A = \pi (2^2) = \pi \cdot 4 = 4\pi \]
Thus, the area of the circle is \( \boxed{4\pi} \).
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