Recall the worksheet on [math]\pi[/math] and radians ([url]http://www.geogebratube.org/material/show/id/29578[/url]). In that worksheet, [math]\pi[/math] is defined to be the ratio of a circle's circumference (C) to its diameter (d). That is, [math]\pi[/math]=C/d. Therefore, C=[math]\pi[/math]d. Since d=2r, you can see that C=2[math]\pi[/math]r.[br][br]The formula for the area of a circle is slightly more difficult do derive. Here are two methods of doing so.