Question
The circumference of a circle is 20π cm. What is the area, in square centimeters? Express your answer in terms of piπ.
Answers
GPT-4o mini
To find the area of a circle given its circumference, we start with the formulas for circumference and area.
1. The formula for the circumference \( C \) of a circle is:
\[
C = 2\pi r
\]
where \( r \) is the radius.
2. We know that the circumference \( C \) is given as \( 20\pi \) cm:
\[
2\pi r = 20\pi
\]
3. To find the radius \( r \), we can divide both sides of the equation by \( 2\pi \):
\[
r = \frac{20\pi}{2\pi} = 10 \text{ cm}
\]
4. Now that we have the radius, we can calculate the area \( A \) using the area formula:
\[
A = \pi r^2
\]
5. Substitute \( r = 10 \) cm into the area formula:
\[
A = \pi (10)^2 = \pi \cdot 100 = 100\pi \text{ square centimeters}
\]
Thus, the area of the circle is
\[
\boxed{100\pi}
\] square centimeters.
1. The formula for the circumference \( C \) of a circle is:
\[
C = 2\pi r
\]
where \( r \) is the radius.
2. We know that the circumference \( C \) is given as \( 20\pi \) cm:
\[
2\pi r = 20\pi
\]
3. To find the radius \( r \), we can divide both sides of the equation by \( 2\pi \):
\[
r = \frac{20\pi}{2\pi} = 10 \text{ cm}
\]
4. Now that we have the radius, we can calculate the area \( A \) using the area formula:
\[
A = \pi r^2
\]
5. Substitute \( r = 10 \) cm into the area formula:
\[
A = \pi (10)^2 = \pi \cdot 100 = 100\pi \text{ square centimeters}
\]
Thus, the area of the circle is
\[
\boxed{100\pi}
\] square centimeters.