Sure, let’s solve this problem step-by-step.
1. Understand the given information and formula:
- We know the area of the circle is 113.04 cm².
- We need to find the circumference of the circle.
- The value of [tex]\(\pi\)[/tex] is given as 3.14.
2. Relevant circle formulas:
- The area [tex]\( A \)[/tex] of a circle is given by [tex]\( A = \pi r^2 \)[/tex], where [tex]\( r \)[/tex] is the radius.
- The circumference [tex]\( C \)[/tex] is given by [tex]\( C = 2 \pi r \)[/tex].
3. Find the radius from the area:
- Rearrange the area formula to solve for the radius:
[tex]\[ r = \sqrt{\frac{A}{\pi}} \][/tex]
- Substitute the given values:
[tex]\[ r = \sqrt{\frac{113.04}{3.14}} \][/tex]
- Calculate:
[tex]\[ r \approx 6.0 \text{ cm} \][/tex]
4. Calculate the circumference using the radius:
- Use the circumference formula:
[tex]\[ C = 2 \pi r \][/tex]
- Substitute the found radius and [tex]\(\pi\)[/tex]:
[tex]\[ C = 2 \times 3.14 \times 6.0 \][/tex]
- Calculate:
[tex]\[ C \approx 37.68 \text{ cm} \][/tex]
Thus, the circumference of the circle is approximately 37.68 cm.
