To find the area of a circle when given its circumference, follow these steps:
1. Identify the relationship between the circumference and the radius:
The formula for the circumference [tex]\( C \)[/tex] of a circle is given by:
[tex]\[
C = 2 \pi r
\][/tex]
where [tex]\( r \)[/tex] is the radius of the circle, and [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159.
2. Rearrange the formula to solve for the radius [tex]\( r \)[/tex]:
[tex]\[
r = \frac{C}{2 \pi}
\][/tex]
Given the circumference [tex]\( C = 12.56 \)[/tex] units, we can substitute this value into the equation to find the radius.
3. Calculate the radius:
[tex]\[
r = \frac{12.56}{2 \pi}
\][/tex]
Upon solving this equation, we get:
[tex]\[
r \approx 1.9989860852342056 \text{ units}
\][/tex]
4. Use the radius to find the area of the circle:
The formula for the area [tex]\( A \)[/tex] of a circle is:
[tex]\[
A = \pi r^2
\][/tex]
Substitute the radius value we found into this formula:
[tex]\[
A = \pi \left(1.9989860852342056\right)^2
\][/tex]
5. Calculate the area:
[tex]\[
A \approx 12.553632615270812 \text{ square units}
\][/tex]
Thus, the area of the circle with a circumference of 12.56 units is approximately 12.553632615270812 square units.
