Surface Area of Spheres
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How to find the surface area of spheres. (Or find radius given surface area.)

This topic is part of the TCS FREE high school mathematics 'How-to Library', and will help you to find the surface area of spheres, or the radius if the surface 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 surface area of a sphere of radius 'r' is given by:

surface area = 4pr2

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

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

surface area = 4pr2

         = 4 3.14 52

         = 314

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

Example 2  if the surface area of a sphere is 500, and p = 3.14, then the radius of the sphere is found as follows:

Method:

Maths Helper Plus can show the calculations and also draw a diagram for calculating the surface area of a sphere given the radius, or for calculating the radius given the surface 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:  'Surface area of sphere.mhp'   File size: 9kb
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:

 

'Surface area of sphere.mhp' solves two kinds of problems:

 

To solve a problem like example 1 above, where you calculate the surface area of a sphere 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, change the value.

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

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

The value in the 'X' edit box must be a '2'. 

If you need to change it, click on the 'X' edit box, change the value.

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

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 sphere, the scale needs to be reduced. In this case, briefly press the F10 key enough times until the whole diagram is seen.

 

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

 

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