Area of a Circle

The circumference (perimeter) of a circle is given by the formula C = 2πr, where r is the radius, and π = 3.141592653... This applet is one way to understand how this leads to the formula for the area of a circle.

We start by dividing a circle into 12 sectors.

• Click on the "rearrange" check box to rearrange the sectors.
• Use the slider to divide the circle into more and more smaller and smaller sectors
• The smaller the sectors, the more the rearranged sectors approximate a rectangle.
• When the sectors are very small, what are the dimensions of the rectangle?
• What is the area of the circle?