Hands-on math!

WHY THE AREA OF A CIRCLE IS R2

(You will need your algebra to prove this!!)



  1. Start with a circle and cut it up into pie slices:
  2. Now roll it out into a line:
    (C)
  3. Now cut the line in half and put the second half upside-down on the first half:
  4. Now it's a RECTANGLE!! (approximately)
    So the area of this rectangle is: 
    
            C     R C
A = R  X   --- = -----
            2      2
  5. Since C = D and D = 2R then substituting 2R for D we have: C = 2R.
    Putting this back in the area formula, we have: 
    
     R C     R(2R)
A = ----- = --------  = RR = R2    <=== Notice that the 2s cancelled!   
       2           2