To find the area of a circle given its circumference, follow these steps:
1. Understand the relationship between the circumference and radius:
The formula for the circumference [tex]\( C \)[/tex] of a circle is [tex]\( C = 2 \pi r \)[/tex], where [tex]\( r \)[/tex] is the radius of the circle.
2. Given the circumference:
[tex]\( C = 18 \pi \)[/tex] feet.
3. Solve for the radius:
[tex]\[
18 \pi = 2 \pi r
\][/tex]
Divide both sides by [tex]\( 2 \pi \)[/tex]:
[tex]\[
r = \frac{18 \pi}{2 \pi} = 9 \text{ feet}
\][/tex]
4. Use the radius to find the area:
The formula for the area [tex]\( A \)[/tex] of a circle is [tex]\( A = \pi r^2 \)[/tex].
Substitute the radius [tex]\( r = 9 \)[/tex] feet into the formula:
[tex]\[
A = \pi (9)^2
\][/tex]
5. Calculate the area:
[tex]\[
A = \pi \times 81 = 81 \pi \text{ square feet}
\][/tex]
So, the area of the circle is [tex]\( 81 \pi \)[/tex] square feet.
