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The measurements of a circle(Circumferance, Area of a circle and a sector, Perimeter of a sector

Updated on October 04, 2010

Circles

 

In this hub we are going to be

looking at the different parts of a

circle and how to calculate each

of them.

 

The Circumference of a Circle,

this is the perimeter of a circle.

 

 

The Diameter = 2 radii

(twice the radius)

 

 

 

 

 

The Radius is half

the Diameter

 

 

 

PERIMETER of a Circle

The formula for the circumference

of a Circle is;

 

  C = TT  D            C  =  2  TT  r

(C = TT  x  D )    ( C = 2  x  TT  x  r)

 

  • The Pi (TT) = 3.141592654

        (check this on a calculator)

 

 

  • (Pi is a special number used to

         calculate distance and area

         when dealing with a circle)

 

 

                                   

  1. Your told that the Diameter is 12cm in the above diagram,

        and you have to find the Circumference to 1 decimal

       place.

 

 

                            C = TT D

 

                            C = TT x 12 = 37.699... (use your calculator)

 

                           C = 37.7 (1 decimal place) ANSWER

 

 

 

2. If the diameter was 12cm that makes the Radius 6cm

    So now we'll calculate the circumference of the same circle

    using the Radius and you have to find the Circumference to

    1 decimal place.

 

 

                                     C = 2 TT r

 

                                     C = 2 x TT x 6 = 37.699....(use your calculator)

 

                                     C = 37.7 (1 decimal place) ANSWER

 

 

AREA of a Circle

 

 

The Area of a Circle is represented by the formula;

 

                                     A = TT r2

 

So using the Circle above as an example;

We know that the Radius is 6cm (½ the Diameter which is 12cm)

 

                                     A = TT r2

                                    

                                     A = TT  x  62

                                   

                                     A = 113.0973355

 

                                     A = 113.1cm2 ( 1 d. p.) ANSWER

 

 

 

 

The red marked part of the circle

is known as an Arc

 

 

 

PERIMETER of a Semi-Circle

 

 

If the arc is a semi-circle our

formula will be C = ½ TT D

 

 

  1. We are asked to find the Perimeter of this Semi-Circle correct to 1 decimal place, and we are told the Diameter is 6cm.

 

 

Now the Perimeter is made up of the Arc(marked with red arrow)

plus the Diameter. So it's two parts to find the Perimeter of this

Semi-Circle.

 

 

         (i) C = ½ TT D (½ because it's a Semi-Circle)

 

             C = ½ x TT x 6 (do this on your calculator)

 

             C = 9.42477

 

 

      (ii) Perimeter = 9.42477 + 6 = 15.42477

 

                              = 15.4 ( 1 d. p.) ANSWER

 

 

 

AREA of a Semi-Circle

 

 

Here we are finding the Area of a Semi-Circle.

 

 

Using the example above we know our Diameter is 6cm

So the Radius will be 3cm (½ the Diameter)

 

 

To find the Area of a Semi-Circle we use the following formula;

 

                                    A = ½ TT r2

 

                                    A = ½ x TT x 32

 

                                    A = 14.137166...

 

                                   A = 14.1cm2 ( 1 d.p.) ANSWER

 

 

PERIMETER of a Quadrant

 

 

A Quadrant is a ¼ of a Circle.

 

If the arc is a Quadrant our

formula will be C = ¼ TT D

 

We are asked to find the Perimeter of this Quadrant correct to 1 decimal place, and we are told the Radius is 8cm.

 

The Diameter is twice the Radius;

Therefore the Diameter is 16cm

 

Now the Perimeter is made up of the Arc

plus the two Radii ( These need to be

added on at the end to the perimeter of

the Quadrant's arc to find the total Perimeter of the Quadrant.

 

So it's two parts to find the Perimeter of

this Quadrant.

 

 

          (i) C = ¼ TT D ( ¼ because its a Quadrant)

 

              C = ¼ x TT x 16

 

              C = 12.56637061 (Perimeter of the arc)

 

 

       (ii)                        Perimeter of ArcRadii Radii

               

                 Perimeter = 12.56637061      +     8     +     8       =     28.566.......

           

                                  = 28.6 ( 1 d. p.) ANSWER

 

 

 

AREA of a Quadrant

 

 

Here we are finding the Area of a Quadrant.

 

 

Using the example above we know our Diameter is 16cm

So the Radius will be 8cm (½ the Diameter)

 

 

To find the Area of a Quadrant we use the following formula;

 

 

                        A = ¼ TT r2 (¼ as its a Quadrant)

 

                       A = ¼ x TT x 82 (use your calculator)

 

                      A = 50.2654......

 

                     A = 50.3 cm2 ( 1 d.p.)  ANSWER

 

 

PERIMETER of Three Quadrants

 

 

This Quadrant is a ¾ of a Circle.

 

Our formula will be C = ¾ TT D

 

 

  1. We are asked to find the Perimeter of this Quadrant correct to 1 decimal place, and we are told the Radius is 10m.

 

 

  • The Diameter is twice the Radius;

        Therefore the Diameter is 20m

 

 

Now the Perimeter is made up of the Arc

plus the two Radii ( These need to be

added on at the end to the perimeter of

the Quadrant's arc to find the total Perimeter of this Quadrant.

 

 

So it's two parts to find the Perimeter of

this Quadrant.

 

 

                   (i) C = ¾ TT D ( ¾ because its three Quadrants)

                      

                       C = ¾ x TT x 20

 

                       C = 47.1238898 (Perimeter of the arc)

 

 

               (ii)              Perimeter of Arc + Radii + Radii

 

          Perimeter  =     47.1238898      +     10   +    10     = 67.123...

 

                             = 67.1m (1 d.p.)

 

 

 

AREA of Three Quadrants

 

 

Here we are finding the Area

of this Quadrant. It has a value

of three Quadrants =  ¾

 

 

Using the example above we know our Diameter is 20m

So the Radius will be 10m  (½ the Diameter)

 

To find the Area of this Quadrant we use the following formula;

 

                    A = ¾ TT r(¾ as its three Quadrants)

 

                    A = ¾  x TT x 102 (use your calculator)

 

                   A = 235.619....

 

                  A = 235.6m2  ( 1 d.p.)

 

 

 

 

 

PERIMETER of a Sector

 

 

Here we are finding the Perimeter

of a Sector, it has a value of

60 degrees.

  1. We are asked to find the Perimeter of this Sector correct

        to 2 decimal places, and we are told the Radius is 15m.

  • The Diameter is twice the Radius;

        Therefore the Diameter is 30m

 

 

Now the Perimeter is made up of the Arc

plus the two Radii ( These need to be

added on at the end, to the perimeter of

the Sector's arc to find the total Perimeter of this Sector.

 

 

  • So it's two parts to find the Perimeter of

       this Sector.

 

 

This time we need to look at the fact we're not dealing with a whole Circle.

 

 

  • In fact we're dealing with a Fraction,

60 / 360 (60 degrees over the whole Circle)

 

 

This is the Fraction part, so let's put this into our formula for Perimeter.

 

 

          (i)                C = 60 / 360 TT D

 

 

                            C = 60 / 360 x TT x 30 (use your calculator)

 

 

                            C = 15.70796... (Perimeter of the arc)

 

 

 

          (ii)          Perimeter of Arc     +     Radii     +     Radii

  

  Perimeter =      15.70796...           +       15        +       15     = 45.707.....

 

 

                      =   45.71m   ( 2 d.p's)   ANSWER

 

 

 

AREA of a Sector

 

 

Here we are finding the Area

of this Sector, it has a Fractional

value of 60 / 360 , to two decimal

places.

Using the example above we know our Diameter is 30m

So the Radius will be 15m (½ the Diameter)

To find the Area of this Sector we'll use the following formula;

                                         A = 60 / 360 TT r2

 

 

                                        A = 60 / 360 TT 152 (use your calculator)

 

 

                                       A = 117.809......

 

 

                                      A = 117.81 m2 ( 2 d.p's.)

 

 

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    • profile image

      Ramraider 6 years ago

      brilliant hub really easy to understand.

    • t.elia profile image
      Author

      t.elia 6 years ago from Northern Ireland

      Hi ramraider, thankyou

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      nazzii 6 years ago

      thnxxx alllotttt yaaah ....noh wrds to say x))))

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      Behishta 5 years ago

      hi!thanks a good and simple way 2 understand......

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      sunil modi 5 years ago

      very nice, thanks for the simple way.sunil modi pune

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      Lucifer 5 years ago

      Very nice web site thanks for the answer!!!!!!

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      Yoorhimmmy~~~~~ 4 years ago

      I loved it!!!~~

    • t.elia profile image
      Author

      t.elia 3 years ago from Northern Ireland

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