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