Question
what is the diameter of a circle that is 21pi
Answers
GPT-4o mini
To find the diameter of a circle when 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. Given that the area \(A = 21\pi\), we can set up the equation:
\[
21\pi = \pi r^2
\]
We can divide both sides by \(\pi\):
\[
21 = r^2
\]
To find the radius \(r\), we take the square root of both sides:
\[
r = \sqrt{21}
\]
The diameter \(d\) of the circle is twice the radius:
\[
d = 2r = 2\sqrt{21}
\]
So, the diameter of the circle is \(2\sqrt{21}\). If you need a numerical approximation, calculating this gives:
\[
2\sqrt{21} \approx 9.165
\]
Thus, the diameter of the circle is \(2\sqrt{21}\), or approximately \(9.165\).
\[
A = \pi r^2
\]
where \(A\) is the area and \(r\) is the radius. Given that the area \(A = 21\pi\), we can set up the equation:
\[
21\pi = \pi r^2
\]
We can divide both sides by \(\pi\):
\[
21 = r^2
\]
To find the radius \(r\), we take the square root of both sides:
\[
r = \sqrt{21}
\]
The diameter \(d\) of the circle is twice the radius:
\[
d = 2r = 2\sqrt{21}
\]
So, the diameter of the circle is \(2\sqrt{21}\). If you need a numerical approximation, calculating this gives:
\[
2\sqrt{21} \approx 9.165
\]
Thus, the diameter of the circle is \(2\sqrt{21}\), or approximately \(9.165\).