To find the correct expression that shows the relationship between the circumference (\(C\)) and the area (\(A\)) of a circle, we need to consider their respective formulas:
1. The circumference of a circle is given by:
\[
C = 2\pi r
\]
where \(r\) is the radius.
2. The area of a circle is given by:
\[
A = \pi r^2
\]
To find the relationship between \(C\) and \(A\), we can express \(r\) from one of these equations and substitute it into the other.
From the circumference formula \(C = 2\pi r\), we can solve for \(r\):
\[
r = \frac{C}{2\pi}
\]
Now, substitute this expression for \(r\) into the area formula \(A = \pi r^2\):
\[
A = \pi \left(\frac{C}{2\pi}\right)^2
\]
Simplify the equation:
\[
A = \pi \left(\frac{C^2}{4\pi^2}\right)
\]
Further simplification gives:
\[
A = \frac{C^2}{4\pi}
\]
So, the correct expression that shows the relationship between the circumference and the area of a circle is:
\[
C^2 = 4\pi A
\]
Thus, the correct answer from the given options is:
\[
C^2 = 4\pi A
\]
Which of the following expressions correctly shows the relationship between the circumference and the area of a circle?(1 point)ResponsesC=2πrupper C equals 2 pi rA=πr2upper A equals pi r squaredC2=4πAupper C squared equals 4 pi upper ACd=π
1 answer