To find the area of a circle with a given circumference of 18.84 units, we will follow these steps:
1. Recall the formula for the circumference of a circle:
[tex]\[
C = 2 \pi r
\][/tex]
where [tex]\( C \)[/tex] is the circumference and [tex]\( r \)[/tex] is the radius of the circle.
2. Given the circumference [tex]\( C = 18.84 \)[/tex] units, we need to find the radius [tex]\( r \)[/tex]. We can rearrange the circumference formula to solve for [tex]\( r \)[/tex]:
[tex]\[
r = \frac{C}{2 \pi}
\][/tex]
3. Substitute the given circumference into the formula to find the radius:
[tex]\[
r = \frac{18.84}{2 \pi}
\][/tex]
Evaluating this, we get:
[tex]\[
r \approx 2.998
\][/tex]
4. Once we have the radius, we can find the area of the circle using the area formula:
[tex]\[
A = \pi r^2
\][/tex]
where [tex]\( A \)[/tex] is the area.
5. Substitute the radius into the area formula to find the area:
[tex]\[
A = \pi (2.998)^2
\][/tex]
Evaluating this expression, we get:
[tex]\[
A \approx 28.245
\][/tex]
Therefore, the area of the circle is approximately [tex]\( 28.245 \)[/tex] square units.
