To find the diameter of a circle when the area is given, you first need to use the formula for the area of a circle, which is:
\[ A = \pi r^2 \]
where \( A \) is the area and \( r \) is the radius. Given that the area \( A = 586 , \text{m}^2 \), you can rearrange the formula to solve for the radius \( r \):
\[ r = \sqrt{\frac{A}{\pi}} \]
Now substituting the area into the formula:
\[ r = \sqrt{\frac{586}{\pi}} \]
Using \( \pi \approx 3.14159 \):
\[ r = \sqrt{\frac{586}{3.14159}} \approx \sqrt{186.56} \approx 13.65 , \text{m} \]
The diameter \( d \) is twice the radius:
\[ d = 2r \approx 2 \times 13.65 \approx 27.3 , \text{m} \]
Rounding to the nearest meter, the diameter is approximately 27 m.
Therefore, the correct answer is:
27 m