To find the area of a circle when given its circumference (C), 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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The formula for the area of a circle is: \[ A = \pi r^2 \]
Given that \( C = 12\pi \), we can find the radius \( r \):
\[ 12\pi = 2\pi r \]
To find \( r \), divide both sides by \( 2\pi \):
\[ r = \frac{12\pi}{2\pi} = 6 \]
Now that we have the radius, we can find the area \( A \):
\[ A = \pi r^2 = \pi (6^2) = \pi \cdot 36 = 36\pi \]
Thus, the area of the circle is \( 36\pi \).
So the answer is 36π.
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