The surface area of a sphere is easy to calculate using the surface area of sphere formula included in this lesson.
If you've already read about the volume of a sphere, you'll know that a sphere is a perfectly round three dimensional shape with all points on its surface equal distance from its center.
This distance, from the center of a sphere to any point on its surface, is the radius (r) of the sphere.
where
The following example calculations will consider the same spherical objects (ping pong, soccer and tennis balls) as volume of a sphere.
SAsphere
= 4πr²
= 4 x π x 2²
= 50.3cm² (square centimeters) to 1 d.p. (one decimal place)
Use the x² button on your calculator to work out 2². The key sequence for the calculation is 4, pi sign (π), 2, x², equals sign (=). 50.26548246 should be displayed which is 50.3 to 1 d.p. To access π and x², you may need to use a shift or 2nd function button.
SAsphere
= 4πr²
= 4 x π x 11²
= 1520.5cm² to 1 d.p.
Grab your calculator, press 4, multiply sign (x), pi sign (π), multiply sign (x), 11, x², equals sign (=).
SAsphere
= 4πr²
= 4 x π x 3.4²
= 145.3cm² to 1 d.p.
The calculator key sequence is the same as for the ping pong / soccer ball calculations except enter 3.4 for the radius (r).
Check out the list below and see if you come up with the same surface areas using your calculator and the surface area of sphere formula SAsphere = 4πr²
Spherical object |
Radius (r) |
Surface area (SAsphere) |
Baseball |
3.7cm |
172.0cm² to 1 d.p. |
Basketball |
12cm |
1809.6cm² to 1 d.p. |
Beach volleyball |
21cm |
5541.8cm² to 1 d.p. |
Now that you've completed the surface area of a sphere lesson, you may wish to take a look at: