To find the area of a circle given the circumference \( C = 12\pi \), we can use the formulas for circumference and area of a circle.
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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 solve for the radius \( r \): \[ 12\pi = 2\pi r \] Dividing both sides by \( 2\pi \): \[ r = \frac{12\pi}{2\pi} = 6 \]
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Now, we can use the radius to find the area of the circle. The formula for the area \( A \) is: \[ A = \pi r^2 \] Substituting \( r = 6 \): \[ A = \pi (6)^2 = \pi \cdot 36 = 36\pi \]
Therefore, the area of the circle is \( 36\pi \).
The correct response is: 36π.