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6.1 Density

GCSE Physics · AQA · Chapter 6: Molecules and Matter

A free GCSE Physics lesson for AQA (8463) from OBA School: mass per unit volume, units and conversions, measuring density, floating and sinking. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Define density and use ρ = m / V with the correct units (kg/m³ or g/cm³)
  • Convert between g/cm³ and kg/m³ and between cm³ and m³, using standard form
  • Rearrange the equation to find the mass (m = ρ V) or the volume (V = m / ρ)
  • Describe how to measure the density of a regular solid, an irregular solid and a liquid
  • Use density to decide whether an object will float or sink in water

Key words

  • Density (ρ): The mass per unit volume of a substance. A dense material packs a lot of mass into a small space.
  • Mass (m): The amount of matter in an object, measured in kilograms (kg) with a balance.
  • Volume (V): The amount of space an object takes up, measured in m³ (or cm³).
  • Displacement: Finding the volume of an object from the rise in water level when it is put under water.
  • Meniscus: The curved surface of a liquid in a narrow tube. Read the scale at the bottom of a water meniscus.
  • Resolution: The smallest change a measuring instrument can show, e.g. 1 mm for a metre rule.

What density means

Two objects can be the same size but have very different masses. A cube of lead is much heavier than a cube of cork with the same volume. We say lead has a greater density. Density is the mass per unit volume of a substance.

density = mass ÷ volume ρ = m / V

ρ = density in kilograms per metre cubed (kg/m³)

m = mass in kilograms (kg)

V = volume in metres cubed (m³)

Rearranged: m = ρ V and V = m / ρ

Worked example: a paving slab

A concrete paving slab is 0.60 m long, 0.40 m wide and 0.050 m thick. Its mass is 27.6 kg. Calculate its density.
V = 0.60 × 0.40 × 0.050 = 0.012 m³
ρ = m / V = 27.6 ÷ 0.012

Answer: 2300 kg/m³

Worked example: the mass of air in a classroom

A classroom is 8.0 m × 6.0 m × 3.0 m. The density of air is 1.2 kg/m³. Calculate the mass of air in the room.
V = 8.0 × 6.0 × 3.0 = 144 m³
m = ρ V = 1.2 × 144 = 172.8 kg

Answer: about 170 kg (2 s.f.) – more than two adults!

Units, conversions and standard form

In the lab, masses are often in grams and volumes in cm³, so density comes out in g/cm³. To use SI units you must convert:

  • mass; Conversion 1 kg = 1000 g; Standard form 1 g = 1 × 10⁻³ kg
  • length; Conversion 1 m = 100 cm; Standard form 1 cm = 1 × 10⁻² m
  • volume; Conversion 1 m³ = 100 × 100 × 100 cm³ = 1 000 000 cm³; Standard form 1 cm³ = 1 × 10⁻⁶ m³
  • density; Conversion 1 g/cm³ = 1000 kg/m³; Standard form multiply g/cm³ by 1000

Worked example: converting a volume and a density

(a) A bottle holds 250 cm³. Write this in m³. 250 × 10⁻⁶ = 2.5 × 10⁻⁴ m³
(b) Aluminium has a density of 2.7 g/cm³. In kg/m³: 2.7 × 1000 = 2700 kg/m³

Answer: 2.5 × 10⁻⁴ m³ and 2700 kg/m³

Worked example: the volume of some oil

What volume does 0.46 kg of olive oil take up? Density of olive oil = 920 kg/m³.
V = m / ρ = 0.46 ÷ 920 = 0.000 50 m³

Answer: 5.0 × 10⁻⁴ m³ (= 500 cm³)

Exam tip: A cube 1 m along each side is 100 cm × 100 cm × 100 cm. That is why 1 m³ is a million cm³, not a hundred.

Measuring the density of a solid

Mass: use an electronic balance. Check it reads zero before you put the object on it.

Volume of a regular solid (cube or cuboid): measure the length, width and height and multiply them. Choose an instrument with a suitable range and resolution.

  • metre rule (mm scale); Typical resolution 1 mm; Good for lengths from a few cm up to 1 m
  • vernier callipers; Typical resolution 0.1 mm; Good for small blocks and diameters up to about 15 cm
  • micrometer; Typical resolution 0.01 mm; Good for very small thicknesses, e.g. wire or foil, up to about 25 mm

Volume of an irregular solid (e.g. a stone): use displacement. Part-fill a measuring cylinder with water and read the volume. Lower the object in on a thread until it is fully under water, then read the volume again. The object’s volume is the rise in the reading. (For bigger objects, use a eureka (displacement) can and collect the water that overflows.)

Worked example: the stone in the diagram

Mass of stone = 48.6 g. Volume = 78.0 − 60.0 = 18.0 cm³
ρ = 48.6 ÷ 18.0 = 2.7 g/cm³

Answer: 2.7 g/cm³ = 2700 kg/m³

Measuring the density of a liquid

Measure a volume of the liquid in a measuring cylinder. Find the mass of an empty beaker, pour in the liquid, then find the mass of the beaker and liquid. The mass of liquid is the difference. (Or put the empty beaker on the balance and press “tare” to zero it.)

Worked example: cooking oil

Volume of oil = 150 cm³. Mass of empty beaker = 62.4 g. Mass of beaker + oil = 200.4 g.
Mass of oil = 200.4 − 62.4 = 138.0 g
ρ = 138.0 ÷ 150 = 0.920 g/cm³

Answer: 0.920 g/cm³ = 920 kg/m³

Floating and sinking

The density of pure water is 1000 kg/m³ (1.0 g/cm³). An object with a density less than this floats in water; an object with a greater density sinks. The closer an object’s density is to water’s, the lower it floats.

Key fact: Density is a property of the material, not the size. Cutting a block of wood in half halves its mass and its volume, so its density stays the same.

Common mistakes

  • Dividing volume by mass. Density = mass ÷ volume; check the unit (kg/m³ is kg divided by m³).
  • Converting cm³ to m³ by dividing by 100. You must divide by 1 000 000 (10⁶).
  • Forgetting to subtract the beaker’s mass when finding the mass of a liquid.
  • Reading a measuring cylinder from above or below, or at the top of the meniscus, instead of at eye level at the bottom of the meniscus.

Revision questions

Try these, then check your answers below each one.

Question 1. What is the definition of density? (Choose from: Mass per unit volume, Volume per unit mass, Weight per unit area, Mass multiplied by volume.)

Answer: Mass per unit volume

Working: Density is mass per unit volume, ρ = m / V. A dense material has a lot of mass in a small volume.

Question 2. A metal block is 0.20 m long, 0.10 m wide and 0.050 m high. Its mass is 2.7 kg. Calculate its density.

Answer: 2700 kg/m³

Working: V = 0.20 × 0.10 × 0.050 = 0.0010 m³. ρ = 2.7 ÷ 0.0010 = 2700 kg/m³.

Question 3. The density of ethanol is 0.79 g/cm³. What is this in kg/m³?

Answer: 790 kg/m³

Working: 1 g/cm³ = 1000 kg/m³, so 0.79 × 1000 = 790 kg/m³.

Related lessons

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