Volume of a sphere

Want to know how to work out the volume of a sphere? Just read on!

Definition of sphere

A perfectly round three dimensional shape with all points on its surface equal distance from its center.

Examples include balls used in sports such as ping pong, soccer and tennis.

Definition of volume of sphere

The amount of three dimensional space occupied by the sphere.

Formula for the volume of a sphere

where

• Vsphere = volume of sphere
• π = pi
• r = radius of sphere

The radius of a sphere is the distance between its center and any point on its surface.

An example calculation

Work out the volume of a ping pong ball with radius (r) 2cm (centimeters).

Vsphere

=   4/3  x  πr³

=   4/3  x  π  x  2³

33.5cm³ (cubic centimeters) to 1 d.p. (one decimal place)

You can use the xy button on your calculator to work out 2³. You may need to press a shift or 2nd function button to access π and xy. The key sequence for the above calculation is 4, divide sign (÷), 3, multiply sign (x), pi sign (π), 2, xy, 3, equals sign (=). Your calculator should display 33.51032164 which is 33.5 to 1 d.p.

Vsphere

=   4/3  x  πr³

=   4/3  x  π  x  11³

5575.3cm³ to 1 d.p.

On your calculator, press 4, divide sign (÷), 3, multiply sign (x), pi sign (π), multiply sign (x), 11, xy, 3, equals sign (=).

And a tennis ball with radius (r) 3.4cm?

Vsphere

=   4/3  x  πr³

=   4/3  x  π  x  3.4³

164.6cm³ to 1 d.p.

The calculator key sequence remains the same as for the ping pong and soccer ball calculations except enter 3.4 for the radius (r).

Let's move on

Think of some other examples of spheres and use their different size radiuses to calculate their volumes.

How about the following? Remember Vsphere = 4/3 x πr³

 Spherical object Radius (r) Volume (Vsphere) Baseball 3.7cm 212.2cm³ to 1 d.p. Basketball 12cm 7238.2cm³ to 1 d.p. Beach volleyball 21cm 38792.4cm³ to 1 d.p.

Enjoyed learning about the volume of a sphere? Next up - the surface area of a sphere.

The following may also be of interest:

Volume of a cone

Surface area of a cone