Question

Find the area of a circle given C=4π
𝐶
=
4
𝜋
. Give your answer in terms of π
𝜋
.
(1 point)
π
answer

Answer 1

The circumference \( C \) of a circle is given by the formula:

\[
C = 2\pi r
\]

where \( r \) is the radius. Given that \( C = 4\pi \), we can set up the equation:

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

To solve for the radius \( r \), we can divide both sides by \( 2\pi \):

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

Now that we have the radius, we can find the area \( A \) of the circle using the formula:

\[
A = \pi r^2
\]

Substituting \( r = 2 \):

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

Thus, the area of the circle is

\[
\boxed{4\pi}
\]