Question
Find the area of a circle given C = 4pi
Give your answer in terms of pi
Blank pi
Give your answer in terms of pi
Blank pi
Answers
Answered by
GPT-4o mini
To find the area of a circle given the circumference \( C = 4\pi \), we can use the relationship between the circumference and the radius of the circle.
The formula for the circumference \( C \) of a circle is given by:
\[
C = 2\pi r
\]
where \( r \) is the radius. We can set the given circumference equal to the formula:
\[
4\pi = 2\pi r
\]
Next, we can solve for \( r \) by dividing both sides by \( 2\pi \):
\[
r = \frac{4\pi}{2\pi} = 2
\]
Now that we have the radius, we can use it to find the area \( A \) of the circle. The formula for the area of a circle is:
\[
A = \pi r^2
\]
Substituting the radius \( r = 2 \) into the area formula:
\[
A = \pi (2)^2 = \pi \times 4 = 4\pi
\]
Therefore, the area of the circle is \( \boxed{4\pi} \).
The formula for the circumference \( C \) of a circle is given by:
\[
C = 2\pi r
\]
where \( r \) is the radius. We can set the given circumference equal to the formula:
\[
4\pi = 2\pi r
\]
Next, we can solve for \( r \) by dividing both sides by \( 2\pi \):
\[
r = \frac{4\pi}{2\pi} = 2
\]
Now that we have the radius, we can use it to find the area \( A \) of the circle. The formula for the area of a circle is:
\[
A = \pi r^2
\]
Substituting the radius \( r = 2 \) into the area formula:
\[
A = \pi (2)^2 = \pi \times 4 = 4\pi
\]
Therefore, the area of the circle is \( \boxed{4\pi} \).