Density and compound measures · Grade 9

In Grade 9 you learn: pressure and converting compound units.

A compound measure combines two quantities: density is mass per unit volume, pressure is force per unit area, and speed is distance per unit time. The same three rearrangements work for all of them.

Key facts

  • Density = mass ÷ volume (g/cm³ or kg/m³).
  • Pressure = force ÷ area (N/m², also called pascals, Pa).
  • Rearranging: mass = density × volume; volume = mass ÷ density; force = pressure × area.
  • 1 g/cm³ = 1,000 kg/m³, and 1 m² = 10,000 cm².
  • km/h → m/s: ÷ 3.6. m/s → km/h: × 3.6.
  • An object floats in water if its density is less than 1 g/cm³.

Worked examples

Example 1

A 250 cm³ block has a mass of 675 g. Find its density.

Answer: 2.7 g/cm³

Example 2

A force of 600 N acts on an area of 40 cm². Find the pressure in N/m².

Answer: 150,000 N/m²

Example 3

Gold has a density of 19.3 g/cm³. Find the mass of a gold bar measuring 2 cm × 3 cm × 1.5 cm.

Answer: 173.7 g

Example 4

50 cm³ of copper (8.9 g/cm³) is melted with 30 cm³ of zinc (7.1 g/cm³). Find the density of the alloy, to 2 decimal places.

Answer: 8.23 g/cm³

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