Question
if the area of a circle is 425 m^2 then what is the length of the diameter to the nearest meter?
Answers
Answered by
GPT-4o mini
To find the diameter of a circle given its 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. In this case, the area \(A\) is given as \(425 \, \text{m}^2\).
1. Rearranging the formula to solve for \(r\):
\[
r^2 = \frac{A}{\pi}
\]
2. Plugging in the area:
\[
r^2 = \frac{425}{\pi}
\]
Using \(\pi \approx 3.14159\):
\[
r^2 \approx \frac{425}{3.14159} \approx 135.8
\]
3. Now, taking the square root to find \(r\):
\[
r \approx \sqrt{135.8} \approx 11.64 \, \text{m}
\]
4. The diameter \(d\) is twice the radius:
\[
d = 2r \approx 2 \times 11.64 \approx 23.28 \, \text{m}
\]
Rounding to the nearest meter:
\[
d \approx 23 \, \text{m}
\]
Therefore, the length of the diameter to the nearest meter is **23 meters**.
\[
A = \pi r^2
\]
where \(A\) is the area and \(r\) is the radius. In this case, the area \(A\) is given as \(425 \, \text{m}^2\).
1. Rearranging the formula to solve for \(r\):
\[
r^2 = \frac{A}{\pi}
\]
2. Plugging in the area:
\[
r^2 = \frac{425}{\pi}
\]
Using \(\pi \approx 3.14159\):
\[
r^2 \approx \frac{425}{3.14159} \approx 135.8
\]
3. Now, taking the square root to find \(r\):
\[
r \approx \sqrt{135.8} \approx 11.64 \, \text{m}
\]
4. The diameter \(d\) is twice the radius:
\[
d = 2r \approx 2 \times 11.64 \approx 23.28 \, \text{m}
\]
Rounding to the nearest meter:
\[
d \approx 23 \, \text{m}
\]
Therefore, the length of the diameter to the nearest meter is **23 meters**.