Exploration: Circumference and Area of a Circle APS
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.
Check the "Show rolling circle" box, then roll the circle with the slider labeled "Roll circle".
Check "Show C measured with r, d."
This leads to a formula for the area of a circle, too. Cut it apart into sectors, and rearrange into a "parallelogram".
Check the last three boxes to see this.
Formulas:
Circumference = diameter (that is, )
Circumference = 2radius (that is, )
Area = Circumference radius
Area = radius squared (that is, )