# Write the area A of a circle as a function

Write the area A of a circle as a function of its circumference C.
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Lupe Kirkland
Step 1
Equation for the circumference of a circle.
$C=2\pi r$
Step 2
Equation for the area of a circle.
$A=\pi {r}^{2}$
Step 3
Solve for r in terms of C.
$C=2\pi r$
$r=\frac{C}{2\pi }$
Step 4
Plug in the equation for r in terms of C into the equation for the area.
$A=\pi {r}^{2}$
$A=\pi {\left(\frac{C}{2\pi }\right)}^{2}$
$A=\frac{{C}^{2}}{4\pi }$
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Abel Maynard
Area of a circle $=A=\left(\pi \right){r}^{2}$
Circumference of a circle $=C=2\left(\pi \right)r$
Where pi is a constant and r is the radius of the circle.
Using these two formulas we can express A in terms of C as follows:
${C}^{2}={\left[2\left(\pi \right)r\right]}^{2}$
$⇒{C}^{2}=4\left[{\left(\pi \right)}^{2}\right]{r}^{2}$
$⇒{C}^{2}=4\left(\pi \right)\left[\left(\pi \right){r}^{2}\right]$
As $\left(\pi \right){r}^{2}=A$
$⇒{C}^{2}=4\left(\pi \right)A$
Therefore: $A=\frac{{C}^{2}}{4\left(\pi \right)}$