To determine the area of a circle when given its circumference, we need to follow a step-by-step approach. Here's a detailed solution:
1. Identify the given information:
- Circumference ([tex]\(C\)[/tex]) of the circle is 9 meters.
2. Recall the formula for the circumference of a circle:
[tex]\[
C = 2\pi r
\][/tex]
where [tex]\(r\)[/tex] is the radius of the circle.
3. Solve for the radius ([tex]\(r\)[/tex]):
[tex]\[
r = \frac{C}{2\pi}
\][/tex]
Given that [tex]\(C = 9\)[/tex]:
[tex]\[
r = \frac{9}{2\pi}
\][/tex]
4. Recall the formula for the area ([tex]\(A\)[/tex]) of a circle:
[tex]\[
A = \pi r^2
\][/tex]
5. Substitute the value of [tex]\(r\)[/tex] into the area formula:
[tex]\[
A = \pi \left(\frac{9}{2\pi}\right)^2
\][/tex]
6. Simplify the expression:
[tex]\[
A = \pi \left(\frac{9^2}{(2\pi)^2}\right)
= \pi \left(\frac{81}{4\pi^2}\right)
\][/tex]
7. Simplify further:
[tex]\[
A = \pi \cdot \frac{81}{4\pi^2}
= \frac{81\pi}{4\pi^2}
\][/tex]
8. Cancel out [tex]\(\pi\)[/tex] in the numerator and the denominator:
[tex]\[
A = \frac{81}{4\pi}
\][/tex]
So, the area ([tex]\(A\)[/tex]) of the circle expressed in terms of [tex]\(\pi\)[/tex] is:
[tex]\[
\boxed{\frac{81}{4\pi}}
\][/tex]
Thus, the area of the circle is [tex]\(\frac{81}{4\pi}\)[/tex] square meters.
