Published: March 23, 2017
Circle cut into 16 slices, underneath  the slices arranged.


This picture demonstrates the famous formula:

Area of a circle = Pi  r2

Here's how to see it:

Look at the slices in the circle - each slice is "r," the radius, long on a side.

Here is what we know before we start:

  • The circumference of the circle is Pi times the diameter.
  • And the diameter is 2 times the radius.
  • So the circumference of the circle is 2 r Pi 

Here is what we do:

  • So now we take the slices and rearrange them into a rectangular like thing.
  • The height is "r" because it is the same length as the radius.

The tricky bit:

  • Think about the width of our rectangle-ish shape.
  • The bottom edge is the "pie crust" of half of the circle.
  • Half the crust on the top edge, half on the bottom.
  • So the width must be HALF the circumference, or Pi  times the radius (or Pi times half of the diameter).
  • Take a minute to think about it - it's a lttle tricky.  
  • What would be a good estimate to the area of this rectangle-ish shape be?  
  • Height times width or     r x (Pi x r)   or...

Area = Pi  r2

To see this more exactly, try to imagine infinite slices (rather than 16) getting infinitely thin.




Open a PDF version that you can cut out yourself