Explain density as mass per unit volume
Compare materials by mass in the same volume rather than by total mass alone.
Exam scope and assessment notes
Mapped to the named 0973 section using teaching from the corresponding single-science course. A 0973-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade. This qualification reports two grades on the 9–1 scale; confirm the entry route for your zone and exam series.
Before you begin
- Recognise mass and volume units.
- Divide to calculate an amount per unit.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which quantity measures occupied space?
What you will learn
- Use density = mass/volume.
- Distinguish mass, volume and density in comparisons.
Density compares how much mass occupies space
Density ρ is mass per unit volume, ρ = m/V. A sample with mass 40.5 g and volume 15 cm³ has density 40.5/15 = 2.7 g/cm³. This means each cubic centimetre of that uniform sample has mass 2.7 g under the stated conditions.
Compare equal volumes to see the meaning directly. Original illustrative samples of volume 100 cm³ with masses 80 g and 270 g have densities 0.80 and 2.70 g/cm³. The second has more mass in the same occupied space. The diagram's boxes have equal schematic volume; they are not measured material samples.
A larger mass does not always mean a larger density
A 100 g sample occupying 20 cm³ has density 5 g/cm³. A 200 g sample occupying 100 cm³ has density 2 g/cm³. The second sample has more total mass but lower density, because its volume increased by more than its mass.
For the same uniform material at unchanged conditions, doubling the sample size doubles both mass and volume, leaving density unchanged. Density can depend on temperature or other conditions; do not present every tabulated value as an exact universal constant. Use the values and conditions supplied in the problem.
Sources for this lesson
Pause and explain
Sample A is 100 g in 20 cm³; B is 200 g in 100 cm³. Which has higher density?
Worked example
Find density for 40.5 g occupying 15 cm³.
Show the worked solution
- Use ρ = m/V.
- Calculate 40.5/15 = 2.7.
- Record 2.7 g/cm³.
Answer 2.7 g/cm³.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Calculate density for 40.5 g and 15 cm³.
Give me a hint
Divide the mass by the volume and keep both unit parts.
Compare my reasoning
- Write ρ = m/V.
- 40.5/15 = 2.7.
- The density is 2.7 g/cm³.
2.7 g/cm³.
Look for these in your work
- Use the correct ratio.
- Attach a density unit.
Compare 100 g in 20 cm³ with 200 g in 100 cm³. Find both densities.
Give me a hint
Evaluate both ratios before comparing masses.
Compare my reasoning
- First density = 100/20 = 5 g/cm³.
- Second density = 200/100 = 2 g/cm³.
- The first is denser despite its smaller mass.
5 g/cm³ and 2 g/cm³; the first is denser.
Look for these in your work
- Calculate both ratios.
- Explain why total mass is insufficient.
A uniform sample is cut into two equal pieces. Explain the change in each piece's mass, volume and density under unchanged conditions.
Give me a hint
Both numerator and denominator scale together.
Compare my reasoning
- Each piece has half the original mass.
- Each occupies half the original volume.
- Their mass/volume ratio and density stay unchanged.
Mass and volume halve; density stays unchanged.
Look for these in your work
- Scale both quantities.
- State unchanged material conditions.
Common mistakes
- Mass alone cannot rank densities when volumes differ.
- Density is mass divided by volume, not their product.
- Density needs both a mass and a volume unit.
What can you explain now?
A 200 g sample occupies 100 cm³. Find density.
Compare with the explanation
2 g/cm³.
Divide mass by the occupied volume.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Describe density without saying simply heavier, then construct a larger-mass but lower-density example.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.