Area of a Circle

Cut the circle into wedges, rearrange into a near-rectangle: area = πr²

Loading...

About This Practice

The circle area formula S = πr² comes from cutting and rearranging: slice the circle into wedges and zip them into an approximate rectangle — the finer the slices, the closer it gets. The rectangle’s width is r and its length about πr, so the area is πr². Switch between 8, 16 and 32 wedges and watch it sharpen.

Tap “Cut & rearrange”: the circle splits into sectors that zip into an approximate rectangle — the finer the cut, the closer it gets. The rectangle's length is about πr and its width is r, so S = πr². Switch between 8, 16 and 32 wedges to watch it sharpen.

HardEstimated Time: 12mincircle areasectorsrearrangeπr²

How to Play

  1. Tap “Cut & rearrange” and watch the circle split into alternating wedges.
  2. Look at the result: what does it resemble? Where does it fall short?
  3. Switch to 16 and then 32 wedges — the shape closes in on a rectangle.
  4. Match the parts: the rectangle’s length ≈ πr (half the circumference), width = r.
  5. Derive the formula: S = πr².

Learning Objectives

More Practices in This Theme

Related Themes for This Grade