Determine liquid density with an empty-container correction
Measure a known liquid volume and isolate its mass by subtraction or a tare.
Exam scope and assessment notes
Core and Extended · Physics 0972, 2026–2028, section 1.4. Density is mass per unit volume. Match the units before calculating. The syllabus includes measuring liquid, regular-solid and sinking irregular-solid densities, then using density data to predict floating. Paper exercises support practical reasoning but do not demonstrate supervised practical competence. Written practice is self-checked; cumulative assessment and human subject-teacher review remain pending. Cambridge states that IGCSE 0972 has the same subject content as IGCSE 0625, with 9–1 grading. This StudyForA pathway maps the 2026–2028 syllabus only. This 9–1 graded qualification is available only in a limited number of administrative zones. Confirm that your centre can enter you for this code and exam series with Cambridge International. Cambridge has published a separate syllabus for 2029. StudyForA has not reconciled that version yet; this page supports exams in 2026, 2027 and 2028 only.
Before you begin
- Read a liquid volume with a suitable scale.
- Subtract empty from filled mass.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How do you isolate liquid mass from empty and filled readings?
What you will learn
- Describe a balance and measuring-cylinder method for liquid density.
- Subtract container mass before calculating.
Isolate the liquid's mass
Measure the empty dry container's mass, then measure the container with a known liquid volume. The difference is the liquid mass. An empty container of 30 g and filled mass 78 g contain 48 g of liquid. If its volume is 60 cm³, density is 48/60 = 0.80 g/cm³.
Alternatively place the empty container on the balance and tare it to zero before adding liquid. The resulting reading can give liquid mass directly, provided the container and reference have not changed. Taring is a reading correction; it does not remove the container physically or change the sample's mass.
Make the mass and volume refer to the same sample
Use a level, upright measuring cylinder and read the water-like concave meniscus bottom at eye level. Keep the sample volume and mass paired: a spill after the volume reading changes the amount whose mass is measured. One approach is weighing the cylinder itself empty and filled so that the final mass and volume refer to the same contained liquid.
Choose sufficient volume for readable measurements, use an appropriately fine scale, and repeat under similar conditions. Avoid assuming a balance's display decimals remove every error. Temperature changes can affect liquid volume and density, so comparisons need matched conditions. These written procedures support a supervised experiment rather than replacing it.
Pause and explain
Empty mass is 30 g, filled mass 78 g and volume 60 cm³. What is liquid density?
Worked example
A container has empty mass 30 g and filled mass 78 g with 60 cm³ liquid. Find liquid density.
Show the worked solution
- Liquid mass = 78 − 30 = 48 g.
- Use the matched liquid volume 60 cm³.
- Density = 48/60 = 0.80 g/cm³.
Answer 0.80 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.
Use empty mass 30 g, filled mass 78 g and volume 60 cm³ to find liquid density.
Give me a hint
Subtract the container before dividing by volume.
Compare my reasoning
- Liquid mass is 48 g.
- ρ = 48/60.
- Density is 0.80 g/cm³.
0.80 g/cm³.
Look for these in your work
- Isolate liquid mass.
- Use the same liquid volume.
An empty cylinder is 42 g. With 50 cm³ liquid its mass is 108 g. Find density.
Give me a hint
Pair the contained liquid's own mass and volume.
Compare my reasoning
- Liquid mass = 108 − 42 = 66 g.
- 66/50 = 1.32.
- Density = 1.32 g/cm³.
1.32 g/cm³.
Look for these in your work
- Subtract the empty cylinder.
- Keep density units.
A 25 cm³ liquid sample in an 18 g container gives total mass 48 g. A learner ignores the container. Compare the incorrect and correct densities.
Give me a hint
The liquid mass is less than the filled mass.
Compare my reasoning
- Incorrect density = 48/25 = 1.92 g/cm³.
- Liquid mass = 48 − 18 = 30 g.
- Correct density = 30/25 = 1.20 g/cm³; the ignored container causes an overestimate.
Incorrect 1.92 g/cm³; correct 1.20 g/cm³.
Look for these in your work
- Calculate both numerators.
- Explain the overestimate.
Common mistakes
- Do not include container mass in liquid density.
- A spill can make mass and volume refer to different amounts.
- Tare the empty container before adding the sample.
What can you explain now?
An empty container is 42 g; filled with 50 cm³ it is 108 g. What is density?
Compare with the explanation
1.32 g/cm³.
Liquid mass is 66 g, so divide by 50 cm³.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Describe both subtraction and tare methods, then explain why the volume must match the weighed liquid.
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.