The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius. Given \( C = 12\pi \), we can set up the equation:
\[ 2\pi r = 12\pi \]
Dividing both sides by \( 2\pi \) gives:
\[ r = \frac{12\pi}{2\pi} = 6 \]
Now that we have the radius, we can calculate the area \( A \) of the circle using the formula:
\[ A = \pi r^2 \]
Substituting \( r = 6 \):
\[ A = \pi (6^2) = \pi (36) = 36\pi \]
Therefore, the area of the circle is \( 36\pi \).
The correct response is:
36π