Question
The area of a circle is 25π ft². What is the circumference, in feet? Express your answer in terms of piπ.
Answers
Answered by
GPT-4o mini
To find the circumference of the circle, we first need to determine its radius using the area formula.
The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]
where \( r \) is the radius.
Given that the area is \( 25\pi \) ft², we can set up the equation:
\[
\pi r^2 = 25\pi
\]
We can divide both sides by \( \pi \) (assuming \( \pi \neq 0 \)):
\[
r^2 = 25
\]
Next, we take the square root of both sides to find the radius:
\[
r = \sqrt{25} = 5 \text{ ft}
\]
Now that we have the radius, we can use the circumference formula to find the circumference \( C \):
\[
C = 2\pi r
\]
Substituting \( r = 5 \) ft into the formula:
\[
C = 2\pi(5) = 10\pi \text{ ft}
\]
Thus, the circumference of the circle is
\[
\boxed{10\pi} \text{ ft}.
\]
The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]
where \( r \) is the radius.
Given that the area is \( 25\pi \) ft², we can set up the equation:
\[
\pi r^2 = 25\pi
\]
We can divide both sides by \( \pi \) (assuming \( \pi \neq 0 \)):
\[
r^2 = 25
\]
Next, we take the square root of both sides to find the radius:
\[
r = \sqrt{25} = 5 \text{ ft}
\]
Now that we have the radius, we can use the circumference formula to find the circumference \( C \):
\[
C = 2\pi r
\]
Substituting \( r = 5 \) ft into the formula:
\[
C = 2\pi(5) = 10\pi \text{ ft}
\]
Thus, the circumference of the circle is
\[
\boxed{10\pi} \text{ ft}.
\]