Find the area of a circle given C=4π

Question

. Give your answer in terms of π
.
(1 point)
π

Answer 1

To find the area of a circle given its circumference \( C \), we can use the following relationships:

1. The formula for the circumference of a circle is: \[ C = 2\pi r \] where \( r \) is the radius of the circle.

2. The formula for the area of a circle is: \[ A = \pi r^2 \]

Given that the circumference \( C = 4\pi \), we can use the circumference formula to solve for the radius \( r \):

\[ 4\pi = 2\pi r \]

Dividing both sides by \( 2\pi \):

\[ r = \frac{4\pi}{2\pi} = 2 \]

Now that we know the radius \( r \), we can substitute it back into the area formula:

\[ A = \pi r^2 = \pi (2^2) = \pi \cdot 4 = 4\pi \]

Thus, the area of the circle is:

\[ \boxed{4\pi} \]