Circumference+and+Area+of+a+circle

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= Circumference =

Circumference is the distance around a circle. This is the circle’s “Perimeter”.

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The Value of Pi

A really important part of working on Circles and spheres is the value of Pi.



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The symbol that looks like an “11″ with a hat on top is called Pi. Pi is defined usually as 3.14.


 * In reality it is really: **

pi = 3.1415926535897932384626433832­795028841971693993751058209749445923078164062862089­98628034825342117067982148086513282306647093844609­55058223172535940812848111745028410270193852110555­96446229489549303819644288109756659334461284756482­33786783165271201909145648566923460348610454326648­21339360726024914127372458700660631558817488152092­09628292540917153643678925903600113305305488204665­21384146951941511609433057270365759591953092186117­38193261179310511854


 * But we just use 3.14**

Pi is a mathematical constant whose value is the ratio of any circle’s circumference to its diameter. Pi = c divided by d.

The most common value used for Pi is 3.14 or 22/7.

How the Pi Number is Determined

An estimation of Pi can be determined by drawing several circles of different sizes, and then measuring their circumferences by running a piece of string around the edge of each circle. We also need to use a ruler to measure the diameter of each circle.

For each circle, we then calculate Circumference divided by Diameter.

The exact value of Pi is best calculated using a computer program, and it has lots of decimals in the answer, that extend endlessly into the billions.

For example Pi rounded off to fifty decimal places is :

3.14159265358979323846264338327950288419716939937510

To read about the fascinating history of Pi, click the link below:

@http://ualr.edu/lasmoller/pi.html


 * The Formula for finding the circumference “C” is: **

C = Pi x Diameter or C = Pi x 2x Radius

We choose which formula to use depending on whether the math question supplies us with Diameter, or with Radius.

Diameter is the distance all the way across a circle.

Radius is the distance from the center to the edge of a circle.

Radius = 1/2 of the Diameter.

The circumference of a circle is the distance around a circle.

Simply the formula for the circumference of a circle is > ** //C=// ** > =//πd//= > =**or**= > =**//C =// //π2r//**=

where //C// is the circumference, //d// is the diameter and //r// is the radius.

If you are given the diameter then use the formula //C = πd//

If you are given the radius then use the formula //C =// 2//πr//

=EXAMPLES=


 * Example 1: **

Find the circumference of the circle with a diameter of 8 cm

Solution:


 * Step 1: Write down the formula: || //C = πd// ||
 * Step 2: Plug in the value: || //C =// 8//π// ||

Answer: The circumference of the circle is 8//π// ≈ 25.163 cm.


 * Example 2: **

Find the circumference of the circle with a radius of 5 cm.

Solution:


 * Step 1: Write down the formula: || //C =// 2//πr// ||
 * Step 2: Plug in the value: || //C =// 10//π// ||

Answer: The circumference of the circle is 10 //π// ≈ 31.24cm.

Here is a rap video on Circumference:

media type="youtube" key="fogehnFNDw0" height="345" width="420"
Now go to the following link and try a few questions on circumference.

[|circumference worksheets]

The following video clip explains circumference, diameter and area of a circle.

media type="youtube" key="jyLRpr2P0MQ" height="345" width="560"

Circumference Games Try this fun basketball game. The Coach will give you a lesson all about Circumference, that you can skip past, and then when you get questions correct, you get basketball shots. Note that to enter your player name, you have to click the mouse into the name box first. Also when shooting, make sure you mouse click and hold down on your player until he is in the air and then release. If he is not off the ground, he will always miss the shot. @http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw41551

Circumference Tests Math Goodies has an online test you can do at the link below: Circumference tests [|Tests] = Area of a Circle =

The formula for the Area of a Circle is:


To determine the Area of any circle we use the calculation: PI x Radius x Radius If we have a Diameter measurement on our circle, you need to halve it to obtain the Radius. A very common mistake is to use the Diameter of a Circle in the area formula.

Here is a music video about circles:media type="youtube" key="eiHWHT_8WrE" height="345" width="420"

Pi is a mathematical constant whose value is the ratio of any circle’s circumference to its diameter.

Eg. Pi = c divided by d.

As stated previously we usually substitute in 3.14 to replace Pi in all of our circle formulas.


 * If we try a Radius of 2.5cm we get an Area of 19.63 sq cm, ie Area = 3.14 x (2.5)2= 19.63cm. **

If we double the Radius to 5cm we obtain Area = 78.53 sq cm.

Notice that doubling the Radius does not double the Area.

The Area is made much bigger than double, because of the r squared in the Area formula.

Click on the following link and try out some area problems.
[|area of a circle]

** Click the link below, and try out the re-sizable circle to calculate areas automatically. **
Interactive Circle



[|Interactive Circle]

Circle Area Games

Try this fun basketball game. The Coach will give you a really good lesson all about Area, when you click the Coach button.

When you are ready to play, click the Play button. After the instructions are given, make sure you click Play again to start the game.

If you get a question correct, the guy automatically shoots a basket.



[|Basketball Game]

Here is a Millionaire Circles Game. This game covers Area, Circumference, and Perimeter.

[|Millionaires Game]

If you want a very challenging Jeopardy Game that covers Circumference and Area then try this one out. Note that to calculate Diameter given Circumference, we need to do Circumference divided by 3.14. To calculate radius we need to work out the square root of (Area divided by3.14) [|Jeopardy]

Circle Area Tests

Math Goodies has a great lesson with examples on Area of a Circle, followed by an online test you can do at the bottom of the page.

@http://www.mathgoodies.com/lessons/vol2/circle_area.html

Here is a more challenging Circles test you can do.

Note that to calculate Diameter given Circumference, we need to do Circumference divided by 3.14.

To calculate radius we need to work out (Area divided by 3.14), and then take the square root of this answer.

@http://www.onlinemathlearning.com/circle-problems.html