Area of a Circle

Image Source: http://www.donaldschwab.com

UFOs are amazing circular shapes, but wouldn’t they have to fly spinning around very fast like a frisbee ? Aliens obviously don’t get dizzy like us humans do!

Let’s start with our favorite music video about circles.

[youtube=http://www.youtube.com/watch?v=eiHWHT_8WrE&w=540&h=433]

The formula for the Area of a Circle is as follows:

Image Source: http://www.learningwave.com

The symbol that looks like an “11” with a hat on top is called Pi.

The Area of any circle is PI x Radius x Radius where Pi is usually set to be 3.14

If we have a Diameter on our circle, then we need to halve it to obtain the Radius.

A very common mistake is to use the Diameter of a Circle in the area formula, which will result in an answer that is way too big.

Here is a great video about how the Area of a Circle formula was figured out by mathematicians.

 

In the following short video, we are shown how to substitute values into our formula and calculate the Area of a Circle.

[youtube=http://www.youtube.com/watch?v=eBAsK9jB91I&w=540&h=433]

 

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

Image Source: http://timthefoolman.files.wordpress.com

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.

Interactive Circle

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

http://www.mathwarehouse.com/geometry/circle/area-of-circle.php

Try a Radius of 2.5cm and get an Area of 19.63 sq cm.
Then double the Radius to 5cm and 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.

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.

http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw41560

Here is a Millionaire Circles Game.

This game covers Area, Circumference, and Perimeter.

http://www.quia.com/rr/281323.html?AP_rand=851196767

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 by 3.14)

http://www.quia.com/cb/10522.html?AP_rand=1241492173&playHTML=1

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

Related Items

Perimeter
Circumference
Area of Simple Shapes
Interesting Circles
Composite Areas
Measurement Formulas
Tall Buildings and Huge Water Dam
My Virtual Home

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Enjoy,
Passy