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Perimeter of a Circle


A circle is a special case.  It involves a different set of rules

  • Firstly make sure you know the difference between a Radius (r) and a Diameter (D)


Radius and Diameter

                                        A Diameter goes from one side of the circle through the centre 
                                                                                  point to the other side.

                                                                            A Radius goes from the centre point of the circle to the outside
                                                                            (the radius is half of the diameter)



  • The perimeter of a circle is  called the circumference


  • The formula for the circumference of a circle is

      C = 2 π r       or      C = π D                         


Where:   π = Pie a constant  = 3.14 or use the pie button on calculator

               r = Radius of a circle

               D = Diameter of a circle



Note:  Which formula you use is up to you!



Example:     Find the circumference of the following circle



                                                                        STEP 1   Formula                   OR           STEP 1    Formula 

                                                                              C = 2 π r                                                  C = π D

                                                                       STEP 2    Substitute                             STEP 2    Substitute

                                                                              C = 2 π 10  (note:  20/2)                           C = π 20

                                                                       STEP 3    Answer                                  STEP 3    Answer

                                                                              C = 62.83 mm                                          C = 62.83 mm


Both formulas give the same answer.  As mentioned you need to know the difference between a radius and a diameter.





Perimeter of Sectors 

  • A sector is a part or fraction of a circle out of 360  e.g  x/360
  • It is like a piece of pie.  In that the you are getting a part of a circle


  •   A semi circle is ½ of a circle which can also be written as 180/360



  • The circle above has a sector with the size of 60 degrees
  • This fraction of the circle is written as:





Example:   Find the perimeter of the following sector (correct to 2 decimal places)



                                                                                STEP 1   Formula                                   

                                                                                              C = ½  x π D           

                                                                                STEP 2    Substitute                              

                                                                                              C = ½ x π x 10 (note the need to add on the side)

                                                                                              C = 15.707….mm + 10         

                                                                                STEP 3    Answer                                  

                                                                                               C = 25.71 mm                       


Example 2:      Find the area Perimeter of the following sector.                                                    


                                                                                STEP 1   Formula                                   

                                                                                              C = 30/360  x π D  (note we are using diameter so we will

                                                                                                                                                                           need to x the radius by 2)
TEP 2    Substitute                              

                                                                                              C = 30/360 x π x 12 (note the need to add on the 2 sides)

                                                                                              C = 3.141….m + 6 + 6          

                                                                                STEP 3    Answer                                  

                                                                                              C = 15.14 m                          


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