Question
Find the radius of a circle with an area of 1,809.56 square centimeters. How did you calculate it? A = πr2
Answers
GPT-4o mini
To find the radius 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. You are given that the area \(A\) is 1,809.56 square centimeters.
1. Start with the area formula and plug in the value for the area:
\[
1,809.56 = \pi r^2
\]
2. To solve for \(r^2\), divide both sides by \(\pi\):
\[
r^2 = \frac{1,809.56}{\pi}
\]
3. Now, use the approximate value of \(\pi \approx 3.14159\):
\[
r^2 \approx \frac{1,809.56}{3.14159} \approx 576.0
\]
4. Next, take the square root of both sides to find \(r\):
\[
r \approx \sqrt{576.0} \approx 24.0
\]
Thus, the radius of the circle is approximately **24.0 centimeters**.
\[
A = \pi r^2
\]
where \(A\) is the area and \(r\) is the radius. You are given that the area \(A\) is 1,809.56 square centimeters.
1. Start with the area formula and plug in the value for the area:
\[
1,809.56 = \pi r^2
\]
2. To solve for \(r^2\), divide both sides by \(\pi\):
\[
r^2 = \frac{1,809.56}{\pi}
\]
3. Now, use the approximate value of \(\pi \approx 3.14159\):
\[
r^2 \approx \frac{1,809.56}{3.14159} \approx 576.0
\]
4. Next, take the square root of both sides to find \(r\):
\[
r \approx \sqrt{576.0} \approx 24.0
\]
Thus, the radius of the circle is approximately **24.0 centimeters**.