Area of Circles
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How to find areas of circles using the formula: A = pr2.

This topic is part of the TCS FREE high school mathematics 'How-to Library', and will help you to find areas of circles using the formula: A = pr2, or to find the radius if the area is given.
(See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Maths Helper Plus software. Click here for instructions.

Theory:

The area of a circle of radius 'r' is given by:

area = pr2

NOTE: The value of p can never be known exactly, so areas of circles cannot be calculated exactly. Common approximations for p are: 3.14, and 22/7.

Example 1  if 'r' = 5 for a given circle, and p = 3.14, then the area of the circle is:

area = pr2

         = 3.14 × 52

         = 78.5

Also, if the area of the circle is known, then the radius can be calculated like this:

Example 2  if the area of a circle is 125, and p = 3.14, then the radius of the circle is found as follows:

Method:

Maths Helper Plus can show the calculations and also draw a diagram for calculating the area of a circle given the radius, or for calculating the radius given the area.  

Step 1 Download the free support file... We have created a Maths Helper Plus document to complement this topic. You can use it to practice the steps described below, and as a starting point for solving your own problems.

File name:  'Area of Circle.mhp'   File size: 8kb
 Click here to download the file.

If you choose 'Open this file from its current location', then Maths Helper Plus should open the document immediately. If not, try the other option: 'Save this file to disk', then run Maths Helper Plus and choose the 'Open' command from the 'File' menu. Locate the saved file and open it. If you do not yet have Maths Helper Plus installed on your computer, click here for instructions.

 

Step 2  Display the parameters box

Press the F5 key to display the parameters box:

 

'Area of Circle.mhp' solves two kinds of problems:

 

To solve a problem like example 1 above, where you calculate the area of a circle given the radius:

The value in the 'X' edit box must be a '1'. If you need to change it, click on the 'X' edit box and change the value.

Click on the 'A' edit box and enter the radius.

To solve a problem like example 2 above, where you calculate the radius of a circle given the area:

The value in the 'X' edit box must be a '2'. If you need to change it, click on the 'X' edit box and change the value.

Click on the 'A' edit box and enter the area of the circle.

Click on the 'B' edit box and type the value of p that you are using. often this will be 3.14, but may also be 22/7. For greatest accuracy, type 'pi' for p.

 

Click the 'Update' button to refresh the diagram and calculations.

 

Step 3  Adjust the scale of the labelled diagram

If the labelled diagram does not display the entire circle, the scale needs to be reduced. In this case, briefly press the F10 key enough times until the whole circle is seen.

 

You can make the diagram bigger by holding down 'Ctrl' while you press F10.

 

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