To find the circumference of a circle given its area, we can use the relationships between the area, radius, and circumference of the circle. Let's go through the steps to solve this problem.
1. Understand the given information:
- Given the area of the circle [tex]\( A = 437.4 \, \text{in}^2 \)[/tex]
- Use [tex]\( \pi \approx 3.14 \)[/tex]
2. Recall the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
3. Solve for the radius [tex]\( r \)[/tex]:
[tex]\[
r^2 = \frac{A}{\pi} = \frac{437.4}{3.14}
\][/tex]
Calculate the fraction on the right-hand side:
[tex]\[
\frac{437.4}{3.14} \approx 139.32
\][/tex]
Now, take the square root to find [tex]\( r \)[/tex]:
[tex]\[
r = \sqrt{139.32} \approx 11.80 \, \text{in}
\][/tex]
4. Recall the formula for the circumference of a circle:
[tex]\[ C = 2 \pi r \][/tex]
5. Substitute the radius [tex]\( r \)[/tex] back into the circumference formula:
[tex]\[
C = 2 \pi \times 11.80
\][/tex]
Using [tex]\( \pi \approx 3.14 \)[/tex]:
[tex]\[
C = 2 \times 3.14 \times 11.80 \approx 74.12 \, \text{in}
\][/tex]
6. Select the closest matching answer:
The closest option to the calculated circumference of 74.12 in is:
[tex]\[
\boxed{74.1 \, \text{in}}
\][/tex]
Therefore, the correct answer is [tex]\( \boxed{74.1 \, \text{in}} \)[/tex].
