Question
If the area of a circle is 586 m2 , then what is the length of the diameter to the nearest meter?(1 point)
Responses
12 m
12 m
293 m
293 m
27 m
27 m
187 m
Responses
12 m
12 m
293 m
293 m
27 m
27 m
187 m
Answers
GPT-4o mini
To find the diameter of a circle given the area, we can use the formula for the area of a circle:
\[ A = \pi r^2 \]
where \( A \) is the area and \( r \) is the radius. We can rearrange the formula to find the radius:
\[ r = \sqrt{\frac{A}{\pi}} \]
Once we have the radius, we can find the diameter \( d \) using the relationship:
\[ d = 2r \]
Given that the area \( A = 586 \, \text{m}^2 \), we can substitute this value into the formula:
1. Calculate the radius:
\[
r = \sqrt{\frac{586}{\pi}} \approx \sqrt{\frac{586}{3.14}} \approx \sqrt{186.54} \approx 13.65 \, \text{m}
\]
2. Calculate the diameter:
\[
d = 2r \approx 2 \times 13.65 \approx 27.3 \, \text{m}
\]
Rounding to the nearest meter gives us a diameter of approximately 27 m.
Thus, the answer is **27 m**.
\[ A = \pi r^2 \]
where \( A \) is the area and \( r \) is the radius. We can rearrange the formula to find the radius:
\[ r = \sqrt{\frac{A}{\pi}} \]
Once we have the radius, we can find the diameter \( d \) using the relationship:
\[ d = 2r \]
Given that the area \( A = 586 \, \text{m}^2 \), we can substitute this value into the formula:
1. Calculate the radius:
\[
r = \sqrt{\frac{586}{\pi}} \approx \sqrt{\frac{586}{3.14}} \approx \sqrt{186.54} \approx 13.65 \, \text{m}
\]
2. Calculate the diameter:
\[
d = 2r \approx 2 \times 13.65 \approx 27.3 \, \text{m}
\]
Rounding to the nearest meter gives us a diameter of approximately 27 m.
Thus, the answer is **27 m**.