Circumference and Area of a Circle

This applet illustrates formulas for the circumference by rolling a circle along a line, then measuring the length in units of the diameter, or the radius.[br][br]Check the "Show rolling circle" box, then roll the circle with the slider labeled "Roll circle".[br]Check "Show C measured with r, d."[br][br]This leads to a formula for the area of a circle, too. Cut it apart into sectors, and rearrange into a "parallelogram".[br][br]Check the last three boxes to see this.
Formulas:[br][br]Circumference = [math]\pi[/math] diameter (that is, [math]C=\pi d[/math])[br]Circumference = 2[math]\cdot\pi\cdot[/math]radius (that is, [math]C=2\pi r[/math])[br][br]Area = Circumference [math]\cdot[/math] radius [br]Area = [math]\pi\cdot[/math] radius squared (that is, [math]A=\pi r^2[/math])

Information: Circumference and Area of a Circle