Density of materials: volume, V, in metres cubed, m³

The idea

Volume measures the space occupied by an object and is measured in cubic metres (m³). In density calculations, volume is the denominator when using ρ = m ÷ V, so a block with mass 2.4 kg and volume 0.003 m³ has density 2.4 ÷ 0.003 = 800 kg/m³. For a regular solid, calculate volume from length × width × height, converting each length to metres first. For example, a block 0.10 m × 0.20 m × 0.15 m has volume 0.003 m³. For an irregular solid, use displacement in a measuring cylinder and convert cm³ to m³ by dividing by 1 000 000. Always label volume with V and m³, and check that the value is reasonable for the object.

What earns the marks

• States that volume is measured in cubic metres (m³) and uses the symbol V correctly in equations.
• Calculates volume of a regular solid using length × width × height, with all lengths in metres.
• Converts volumes given in cm³ to m³ by dividing by 1 000 000 before substituting into ρ = m ÷ V.
• Uses volume as the denominator in the density equation and keeps the unit m³ consistent with mass in kg to give density in kg/m³.
• Measures volume of an irregular solid by displacement and records the result with the unit m³.

Common mistakes and how to put them right

• Using cm³ directly in ρ = m ÷ V with mass in kg.

  Put it right by converting cm³ to m³ by dividing by 1 000 000.

• Multiplying length, width and height without converting each to metres.

  Put it right by converting every length to metres before multiplying.

• Confusing volume with capacity in litres.

  Put it right by converting litres to m³ using 1 litre = 0.001 m³.

Exam tips

• Write the volume formula or displacement method before substituting numbers, so the unit conversion is visible.
• Convert all lengths to metres at the start of a regular-solid calculation to avoid mixing cm and m.
• Check that the final density unit is kg/m³ when volume is in m³ and mass is in kg.