How to find the ratio of diameter and circumference

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SAT Math › How to find the ratio of diameter and circumference

1 - 1

Let represent the area of a circle and represent its circumference. Which of the following equations expresses in terms of ?

$\frac{C^2}{\pi}$

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

CORRECT

$\frac{C}{4\pi}$

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

Explanation

The formula for the area of a circle is $A=\pi r^2$ , and the formula for circumference is $C=2\pi r$ . If we solve for C in terms of r, we get
$r=C/2\pi$ .

We can then substitute this value of r into the formula for the area:

$A=\pi r^2$

$=\pi (C/2\pi )^2$

$=C^2\pi /4\pi ^2$

$=C^2/4\pi$

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