To find the area of the 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 find the area \( A \) of the circle using the formula: \[ A = \pi r^2 \] Plugging in the radius we found: \[ A = \pi (6)^2 = \pi \cdot 36 = 36\pi \]
Thus, the area of the circle is \( 36\pi \).
So the correct response is: 36π
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