Read liquid volumes and find displacement volumes
Use a measuring cylinder's scale and take a difference to measure an irregular solid's volume.
Section P1.1 · Physical quantities and measurement techniques
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
- Subtract readings in the same unit.
- Recognise volume as occupied space.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which is a unit of volume?
What you will learn
- Read the bottom of a water meniscus at eye level.
- Calculate a submerged solid's volume by displacement.
Read the liquid surface consistently
Stand a measuring cylinder upright on a level surface and identify the value of a small scale interval. For water with a concave meniscus, read the bottom of the curve at eye level. The curved surface must not be mistaken for a single flat level at its highest edges.
Choose a cylinder with sufficient capacity and a suitably fine scale for the volume. A reading such as 38 cm³ is a volume, whereas the liquid height in centimetres is a length. One millilitre is one cubic centimetre. These unit names can describe the same volume; a centimetre alone cannot.
Subtract initial from final volume
An irregular solid that sinks and does not dissolve can be fully submerged in water. Record the initial water volume, lower the solid carefully without splashing, and record the new reading with the same eye-level method. The rise is the solid volume, provided no water is lost and no air is trapped on the object.
For readings of 38 cm³ and 54 cm³, the solid volume is 16 cm³. The final reading is the total liquid-plus-solid occupied volume, not the solid volume by itself. An object that floats needs another method to keep it fully submerged and account for any extra object; simply reading a partly floating object's displacement does not give its whole volume.
Sources for this lesson
Pause and explain
A submerged stone changes the cylinder reading from 38 to 54 cm³. What is its volume?
Worked example
Water rises from 38 cm³ to 54 cm³ when an insoluble stone is fully submerged. Find the stone volume.
Show the worked solution
- Check that the object is fully submerged and no water is lost.
- Subtract 54 − 38.
- State a volume unit: 16 cm³.
Answer 16 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.
Water changes from 38 cm³ to 54 cm³ around a submerged stone. Find the stone volume.
Give me a hint
Use the change in cylinder reading rather than the final total.
Compare my reasoning
- Identify initial and final readings.
- Subtract 54 − 38 = 16.
- Attach cm³ and state the full-submersion assumption.
16 cm³.
Look for these in your work
- Use a difference.
- Keep a volume unit.
A metal piece raises 47 ml of water to 65 ml. Find its volume in cm³.
Give me a hint
A millilitre is the same volume as a cubic centimetre.
Compare my reasoning
- The increase is 65 − 47 = 18 ml.
- Convert with 1 ml = 1 cm³.
- The piece volume is 18 cm³ if no water is lost.
18 cm³.
Look for these in your work
- Subtract correctly.
- Use the volume equivalence.
Air bubbles cling to a stone during displacement. Predict the direction of error and suggest an improvement.
Give me a hint
The final rise includes anything excluding water, including trapped air.
Compare my reasoning
- Air bubbles displace water as well as the stone.
- The measured increase overestimates the stone's volume.
- Remove trapped bubbles and repeat the initial-to-final measurement without splashing.
An overestimate; remove bubbles and repeat carefully.
Look for these in your work
- Identify the error direction.
- Suggest an improvement addressing the bubbles.
Common mistakes
- Read the bottom of a concave water meniscus, not its raised edges.
- Do not use the final cylinder reading alone for a solid.
- Trapped air adds displaced volume.
What can you explain now?
A cylinder reading changes from 26 ml to 41 ml. What volume is displaced?
Compare with the explanation
15 cm³.
The increase is 15 ml and 1 ml equals 1 cm³.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Describe a cylinder reading and explain three conditions needed for reliable solid displacement.
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.