ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

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

Updated on October 4, 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.)

 

 

Comments

    0 of 8192 characters used
    Post Comment

    • t.elia profile imageAUTHOR

      t.elia 

      4 years ago from Northern Ireland

    • profile image

      Yoorhimmmy~~~~~ 

      5 years ago

      I loved it!!!~~

    • profile image

      Lucifer 

      6 years ago

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

    • profile image

      sunil modi 

      6 years ago

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

    • profile image

      Behishta 

      7 years ago

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

    • profile image

      nazzii 

      7 years ago

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

    • t.elia profile imageAUTHOR

      t.elia 

      7 years ago from Northern Ireland

      Hi ramraider, thankyou

    • profile image

      Ramraider 

      7 years ago

      brilliant hub really easy to understand.

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://hubpages.com/privacy-policy#gdpr

    Show Details
    Necessary
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Marketing
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Statistics
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)