Question
If the area of a circle is 425 m², then what is the length of the diameter to the nearest meter? ( A = π * r² ) (1 point) Responses 12 m 12 m 23 m 23 m 135 m 135 m 13 m
Answers
Answered by
GPT-4o mini
To find the diameter of the circle when the area is given, you can use the formula for the area of a circle:
\[
A = \pi r^2
\]
Given that the area \( A = 425 \, m^2 \), we can rearrange the formula to solve for the radius \( r \):
\[
r^2 = \frac{A}{\pi} = \frac{425}{\pi}
\]
Calculating this:
\[
r^2 \approx \frac{425}{3.14} \approx 135.24
\]
Now, take the square root to find the radius \( r \):
\[
r \approx \sqrt{135.24} \approx 11.62 \, m
\]
The diameter \( d \) is twice the radius:
\[
d = 2r \approx 2 \times 11.62 \approx 23.24 \, m
\]
Rounding to the nearest meter, the diameter is:
\[
d \approx 23 \, m
\]
Thus, the length of the diameter to the nearest meter is **23 m**.
\[
A = \pi r^2
\]
Given that the area \( A = 425 \, m^2 \), we can rearrange the formula to solve for the radius \( r \):
\[
r^2 = \frac{A}{\pi} = \frac{425}{\pi}
\]
Calculating this:
\[
r^2 \approx \frac{425}{3.14} \approx 135.24
\]
Now, take the square root to find the radius \( r \):
\[
r \approx \sqrt{135.24} \approx 11.62 \, m
\]
The diameter \( d \) is twice the radius:
\[
d = 2r \approx 2 \times 11.62 \approx 23.24 \, m
\]
Rounding to the nearest meter, the diameter is:
\[
d \approx 23 \, m
\]
Thus, the length of the diameter to the nearest meter is **23 m**.