Density (CIE IGCSE Physics: Co-ordinated Sciences (Double Award))

• Density is defined as:

The mass per unit volume of a material

• Density is related to mass and volume by the following equation:

• Where:
  • ρ = density, measured in kilograms per metre cubed (kg m⁻³)
  • m = mass, measured in kilograms (kg)
  • V = volume, measured in metres cubed (m³)

Formula triangle for density, mass and volume

To use a formula triangle, simply cover up the quantity you wish calculate and the structure of the equation is revealed

• For more information on how to use a formula triangle, refer to the revision note on Speed and velocity

• Objects made from low density materials typically have a low mass
• Similarly sized objects made from high density materials have a high mass
  • For example, a bag full of feathers is far lighter compared to the same bag full of metal
  • Or another example, a balloon is less dense than a small bar of lead despite occupying a larger volume

• Gases, for example, are generally less dense than solids because the particles in a gas are more spread out (same mass, over a larger volume)

Comparing the density of solids and gases

A gas is less dense than the same substance in liquid or solid form

• The units of density depend on what units are used for mass and volume:
  • If the mass is measured in g and volume in cm³, then the density will be in g/cm³
  • If the mass is measured in kg and volume in m³, then the density will be in kg/m³

Determining volume to calculate density

• The volume of an object may not always be given directly, but can be calculated with the appropriate equation depending on the object’s shape

Common formulae required to calculate the volumes of objects

Volumes of common 3D shapes