# 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