Question

use the formula for the circumference of a circle to write a formula for the area of a circle in terms of its circumference

Answer 1

Answer:

$A=\frac{C^2}{4\pi ^2}$

Step-by-step explanation:

Recall to find the circumference of a circle the formula is $C=\pi d$ or $C=2\pi r$. We will also need the formula for the area of a circle which is $A=\pi r^{2}$. Since the area formula is in terms of r we will use the second formula for circumference.

We start by solving for r in the Circumference formula.

$C=2\pi r\\\frac{C}{2\pi } =r$. We input this value of r into the area formula.

$A=\pi r^{2} \\A=\pi (\frac{C}{2\pi })^2\\A=\pi (\frac{C^2}{4\pi ^2 })\\A=\frac{C^2}{4\pi ^2}$