To find the area of a circle given its circumference, follow these steps:
1. Identify the given information:
- The circumference [tex]\( C \)[/tex] of the circle is 4 kilometers.
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. Rearrange the formula to solve for the radius [tex]\( r \)[/tex]:
- [tex]\( r = \frac{C}{2 \pi} \)[/tex].
4. Calculate the radius:
- Substitute [tex]\( C = 4 \)[/tex] into the formula:
[tex]\[
r = \frac{4}{2 \pi} \approx 0.6366 \text{ (to four decimal places)}
\][/tex]
5. Recall the formula for the area [tex]\( A \)[/tex] of a circle:
- [tex]\( A = \pi r^2 \)[/tex].
6. Calculate the area using the radius found:
- Substitute [tex]\( r \approx 0.6366 \)[/tex] into the area formula:
[tex]\[
A = \pi (0.6366)^2 \approx 1.2732 \text{ (to four decimal places)}
\][/tex]
7. Round the area to the nearest tenth:
- The value 1.2732 rounded to the nearest tenth is 1.3.
Thus, the area of the circle is [tex]\( \boxed{1.3 \, \text{km}^2} \)[/tex].
