To find the area of the circle, we can use the relationship between the circumference \( C \) and the radius \( r \), as well as the formula for the area \( A \) of a circle.
The formula for the circumference of a circle is given by:
\[ C = 2\pi r \]
You provided:
\[ C = 12\pi \]
We can set these equal to each other:
\[ 2\pi r = 12\pi \]
To solve for \( r \), divide both sides by \( 2\pi \):
\[ r = \frac{12\pi}{2\pi} = 6 \]
Next, we can use the radius to find the area \( A \) of the circle. The formula for the area is:
\[ A = \pi r^2 \]
Substituting the value of \( r \):
\[ A = \pi (6^2) = \pi \times 36 = 36\pi \]
Thus, the area of the circle is \( 36\pi \).
The correct response is:
36π