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
27 m
27 m
293 m
293 m
12 m
12 m
187 m
187 m
Responses
27 m
27 m
293 m
293 m
12 m
12 m
187 m
187 m
Answers
GPT-4o mini
To find the diameter of a circle given its area, you can use the formula for the area of a circle:
\[
A = \pi r^2
\]
where \( A \) is the area and \( r \) is the radius.
Given that the area \( A = 586 \, m^2 \), we can solve for \( r \):
\[
r^2 = \frac{A}{\pi}
\]
Substituting the values:
\[
r^2 = \frac{586}{\pi}
\]
Calculating \( \pi \) (approximately 3.14):
\[
r^2 \approx \frac{586}{3.14} \approx 186.64
\]
Now, taking the square root to find \( r \):
\[
r \approx \sqrt{186.64} \approx 13.65 \, m
\]
The diameter \( d \) is twice the radius:
\[
d = 2r \approx 2 \times 13.65 \approx 27.3 \, m
\]
To the nearest meter, the length of the diameter is:
\[
\boxed{27 \, m}
\]
\[
A = \pi r^2
\]
where \( A \) is the area and \( r \) is the radius.
Given that the area \( A = 586 \, m^2 \), we can solve for \( r \):
\[
r^2 = \frac{A}{\pi}
\]
Substituting the values:
\[
r^2 = \frac{586}{\pi}
\]
Calculating \( \pi \) (approximately 3.14):
\[
r^2 \approx \frac{586}{3.14} \approx 186.64
\]
Now, taking the square root to find \( r \):
\[
r \approx \sqrt{186.64} \approx 13.65 \, m
\]
The diameter \( d \) is twice the radius:
\[
d = 2r \approx 2 \times 13.65 \approx 27.3 \, m
\]
To the nearest meter, the length of the diameter is:
\[
\boxed{27 \, m}
\]