How to find the ratio of diameter and circumference - PSAT Math

Card 0 of 1

Question

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

Answer

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:

$A=\pi r^2$

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

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

$=C^2/4\pi$

Compare your answer with the correct one above

Tap the card to reveal the answer