The Circle

A circle is a plane figure in which all points on it are the same distance from the center.

The RADIUS "R" is the distance from the center to the edge.

The DIAMETER "D" is the distance across the circle.

The CIRCUMFERENCE "C" is the distance around the edge of the circle.
It's the perimeter of the circle.
The diameter "D" is twice the radius "R" or

D = 2 R

The circumference "C" is ("pi") times the diameter "D"

C = D

is 3.1415926...(goes on forever), but just use 3.14 for

The area "A" of a circle is:
A = RR or ...
A = R2

So, for a circle whose radius "R" is 6 inches:














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:


  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 = 2R, we have:
    
         R C     R(2R)
    A = ----- = --------  = RR = R2
          2         2
    
(Notice that the 2's cancelled)