Surface area of a sphere


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.


Formula for surface area of a sphere


where

  • SAsphere = surface area of sphere
  • π = pi
  • r = radius of sphere


The following example calculations will consider the same spherical objects (ping pong, soccer and tennis balls) as volume of a sphere.


Surface area of a ping pong ball with radius (r)
2 centimeters (cm)

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.


Surface area of a soccer ball with radius (r) 11cm


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 (=).


Surface area of a tennis ball with radius (r) 3.4cm


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).


Other surface area of sphere calculations


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:


Volume of a sphere

Volume of a cone

Surface area of a cone

Volume of a cylinder

Surface area of a cylinder


Back to top


› Surface area of a sphere