To find the area of a circle given its circumference, we proceed through several steps. Here's the detailed method:
1. Find the radius of the circle:
- The circumference of a circle is given by the formula [tex]\( C = 2\pi r \)[/tex], where [tex]\( C \)[/tex] is the circumference and [tex]\( r \)[/tex] is the radius.
- We are given the circumference [tex]\( C = 18.84 \)[/tex] units.
- Rearranging the formula to solve for the radius [tex]\( r \)[/tex], we get:
[tex]\[
r = \frac{C}{2\pi}
\][/tex]
- Substituting the given values:
[tex]\[
r = \frac{18.84}{2\pi}
\][/tex]
- This calculation yields:
[tex]\[
r \approx 2.9984791278513083 \text{ units}
\][/tex]
2. Calculate the area of the circle:
- The area [tex]\( A \)[/tex] of a circle is given by the formula [tex]\( A = \pi r^2 \)[/tex].
- Using the radius we found:
[tex]\[
A = \pi \left(2.9984791278513083\right)^2
\][/tex]
- This calculation yields:
[tex]\[
A \approx 28.245673384359325 \text{ square units}
\][/tex]
Thus, the area of the circle with a circumference of 18.84 units is approximately [tex]\( 28.245673384359325 \)[/tex] square units.
