
How to find the surface area of spheres. (Or find radius given surface area.)
Theory:The surface area of a sphere of radius 'r' is given by:
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:
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 2 Display the parameters boxPress 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:
To solve a problem like example 2 above, where you calculate the radius of a sphere given the surface area:
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 diagramIf 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.
