To find the diameter of a circle given its area, you can use the following steps:
1. Identify the formula for the area of a circle:
[tex]\[ \text{Area} = \pi \times r^2 \][/tex]
where [tex]\( \text{Area} \)[/tex] is the area of the circle, [tex]\( \pi \approx 3.14159 \)[/tex], and [tex]\( r \)[/tex] is the radius of the circle.
2. Rearrange the formula to solve for the radius [tex]\( r \)[/tex]:
[tex]\[ r = \sqrt{\frac{\text{Area}}{\pi}} \][/tex]
3. Substitute the given area into the formula:
[tex]\[ r = \sqrt{\frac{78.5}{\pi}} \][/tex]
4. Calculate the radius:
Using the given area of 78.5 square meters, find the radius:
[tex]\[ r \approx 4.998732445873411 \, \text{meters} \][/tex]
5. Calculate the diameter:
The diameter [tex]\( d \)[/tex] of a circle is twice the radius:
[tex]\[ d = 2 \times r \][/tex]
Substituting the radius:
[tex]\[ d \approx 2 \times 4.998732445873411 \][/tex]
[tex]\[ d \approx 9.997464891746821 \, \text{meters} \][/tex]
6. Round the diameter to the nearest meter:
[tex]\[ d \approx 10 \, \text{meters} \][/tex]
So, the diameter of the circle, rounded to the nearest meter, is [tex]\( 10 \)[/tex] meters. Therefore, the correct answer is:
O 10 meters
