Determine density of regularly shaped solids
Measure the mass and calculate geometric volume before forming the density ratio.
Section 1.4 · Density
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
- Calculate cuboid and cylinder volumes.
- Use density = mass/volume.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which formula gives a cuboid's volume?
What you will learn
- Describe a mass and dimension method for a regular solid.
- Use appropriate volume formulas and consistent units.
Measure dimensions and mass separately
For a uniform cuboid, measure length, width and height with a suitable ruler, viewing each scale correctly, and measure its mass using a zeroed balance. Multiply the three perpendicular dimensions to find volume. A sample 5.0 cm by 4.0 cm by 6.0 cm has volume 120 cm³; at mass 324 g its density is 2.7 g/cm³.
Check that the geometric shape represents the actual solid. A box with a cavity does not have the same material volume as a solid block with equal outside dimensions. Repeated dimension measurements can reveal uneven surfaces; use the stated appropriate mean dimensions and explain limitations rather than pretending every object is a perfect cuboid.
Use the volume formula for the shape
For a cylinder, V = πr²h; if a diameter is measured, halve it before squaring. A sample of radius 1.5 cm and height 10 cm has volume 22.5π cm³. With mass 180 g, density is 8/π ≈ 2.55 g/cm³. Keep sufficient calculation precision until the final rounded result.
A thin rectangular sheet with length 5 cm, width 4 cm and thickness 2 mm needs a thickness conversion to 0.2 cm. Its volume is 4 cm³, not 40 cm³. Choose instruments able to resolve small dimensions; a multiples method can estimate a thin repeated thickness when applicable. Describe the improvement and the assumption behind it.
Pause and explain
A cylinder has diameter 3.0 cm and height 10 cm. Which is its volume?
Worked example
A solid cuboid is 5.0 × 4.0 × 6.0 cm and has mass 324 g. Find density.
Show the worked solution
- V = 5 × 4 × 6 = 120 cm³.
- ρ = 324/120.
- Density = 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.
Find density of a 324 g cuboid measuring 5.0 × 4.0 × 6.0 cm.
Give me a hint
Calculate the volume before dividing mass by it.
Compare my reasoning
- Volume is 120 cm³.
- 324/120 = 2.7.
- Density is 2.7 g/cm³.
2.7 g/cm³.
Look for these in your work
- Use all three dimensions.
- Divide mass by volume.
A cylinder has diameter 3.0 cm, height 10 cm and mass 180 g. Find its density.
Give me a hint
Halve the diameter before using πr²h.
Compare my reasoning
- Radius is 1.5 cm.
- Volume is 22.5π cm³.
- Density = 180/(22.5π) = 8/π ≈ 2.55 g/cm³.
8/π g/cm³, approximately 2.55 g/cm³.
Look for these in your work
- Use radius correctly.
- Round only after the ratio.
A solid sheet is 5 cm by 4 cm by 2 mm and has mass 10.8 g. Find density and explain the consequence of treating 2 mm as 2 cm.
Give me a hint
Convert the thickness before forming its volume.
Compare my reasoning
- 2 mm = 0.2 cm; volume = 4 cm³.
- True density = 10.8/4 = 2.7 g/cm³.
- Using 2 cm makes volume ten times too large and density ten times too small.
2.7 g/cm³; the unit error would give 0.27 g/cm³.
Look for these in your work
- Convert the thickness.
- Explain the density error direction.
Common mistakes
- Three lengths produce volume, not surface area.
- A cylinder uses radius, not diameter, in πr²h.
- Convert a millimetre thickness before multiplying centimetre dimensions.
What can you explain now?
A 5 cm × 4 cm × 2 mm sheet has what volume?
Compare with the explanation
4 cm³.
Use thickness 0.2 cm to match the other dimensions.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Describe the full cuboid method and one instrument or shape limitation.
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.