Determine density of regularly shaped solids
Measure the mass and calculate geometric volume before forming the density ratio.
Section P1.4 · Density
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
- 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.
Sources for this lesson
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.