Did you know that a floating plastic block can move the water level by 18 millilitres even though the block itself occupies 36 cubic centimetres? Both numbers can be correct. The first measures the water displaced while it floats; the second describes all the space taken up by the block. Confusing the two is a wonderfully instructive science mistake.
Full object volume means the total space occupied by an object, including the portion above water. Floating displacement volume means only the volume of fluid the object pushes aside while it is floating. To measure the full volume of a waterproof floating solid by water displacement, submerge it completely, measure the combined displacement with a separate sinker, and subtract the sinker’s displacement measured on its own. Do not mistake the water displaced by a floating object for its complete volume.
Start with the question a learner can actually answer
Place a small, clean, waterproof plastic block into a transparent container. It floats with its top above the water. Ask: ‘Does the water rise as though the entire block were under the surface?’ Encourage the learner to point to the submerged portion before answering. The water level rises because submerged material displaces water. Yet the portion sticking out into the air has not displaced water.
The first diagnostic is not a formula. Ask a student to draw the waterline through a floating block, label the part below the surface, then label the whole block. If both labels are given the same name, the obstacle is conceptual. It will not be fixed by asking for a more accurate subtraction.
Why the physics makes the two measurements different
A floating body settles when upward buoyancy balances its weight. Under Archimedes’ principle, the buoyant force equals the weight of the displaced fluid. In ordinary freshwater, one millilitre of water has a mass of approximately one gram, so a floating block with mass 18 g will typically displace about 18 mL of water, provided it is floating freely and not touching a support. This is an approximate classroom relationship, not a precision calibration rule for every temperature or fluid.
Imagine that same block has a complete geometric volume of 36 cm³. Its average density is 18 g divided by 36 cm³, or 0.50 g/cm³. Since that is below the approximate 1 g/cm³ density of freshwater, the block floats. Roughly half its volume must be submerged to displace water weighing 18 g. If a learner writes ‘the volume of the block is 18 cm³’ after only observing it float, the learner has answered a different question.
The US National Oceanic and Atmospheric Administration’s classroom buoyancy activity explains the relationship between displacement, weight and floating. OpenStax’s treatment of Archimedes’ principle distinguishes partially and fully submerged objects. Our block numbers are invented to teach the calculation; they are not measurements from those sources.
A worked laboratory record: two readings, one subtraction
Here is a fictional demonstration using a sufficiently large, transparent, graduated vessel, freshwater, a waterproof block and a small, non-absorbent sinker secured so both objects can be lowered safely. The same sinker stays completely immersed during both relevant trials. Assume the suspension cord contributes negligible displacement and no air bubbles cling to the objects. Read the bottom of the meniscus at eye level where the vessel’s design calls for it.
- Water without either object: 150 mL. This is the baseline, not the block’s volume.
- Water with the sinker fully submerged on its own: 173 mL. Therefore sinker displacement = 173 − 150 = 23 mL.
- Water with that same sinker and the entire floating block both fully submerged: 209 mL. Therefore combined displacement = 209 − 150 = 59 mL.
- Block’s full volume = combined displacement − sinker displacement = 59 − 23 = 36 mL, equivalent to 36 cm³.
- Independent arithmetic check: 209 − 173 = 36 mL directly, because the sinker and starting water volume appear in both readings.
This is a subtraction of two compatible measurements, made with the same container and sinker. We are not subtracting the mass of the sinker from its displaced volume. A 23 mL displacement is a volume; a sinker labelled 40 g would have a mass. Those are different physical quantities.
Suppose the same block has a measured dry mass of 18 g. Then the illustrative density is 18 ÷ 36 = 0.50 g/cm³. An observation of about 18 mL floating displacement is consistent with that mass in approximately 1 g/mL freshwater, but it is not the 36 mL total volume. The two different displacement results tell a coherent story rather than revealing a broken experiment.
What changes when you hold the block down?
When a student pushes the block below the surface, more of it displaces water. Once the full block is underwater, its displaced water volume equals the external volume of the block, assuming no trapped air or water absorption. That is the useful moment for a volume measurement. It does not mean the block has become heavier merely because it is farther down: its mass has not changed. Additional downward force is needed to keep a buoyant object immersed.
Do not ask children to hold a block under water with a finger while reading a narrow meniscus. The finger also displaces water, changes the level, and creates a potentially large error. Use an appropriate teacher-managed non-absorbent sinker and repeat its measurement separately. A broad mouth vessel or an overflow displacement setup may be better for large irregular objects.
Why doing the sinker trial first matters
A useful learner mistake is to record only ‘209 mL with everything in the water’ and subtract 150 mL to report a 59 mL block. That answer includes the sinker. The fact that the block could not be submerged unaided does not make the sinker invisible. Its displacement must be removed, just as the weight of a container is removed when calculating net mass.
Ask learners to write three labels, not three unlabelled numbers: initial water, sinker-only, and sinker-plus-object. Make them say which difference answers which physical question. A pair of unexplained subtractions is an incomplete scientific explanation even if it accidentally reaches 36.
A progression from guided practice to an independent check
Guided task: separate what is seen from what is calculated
First let the learner see the floating waterline. Point to the water pushed aside and ask why the portion above water does not contribute to the observed level rise. Next display the three fictional readings above. Work the 23 mL sinker displacement together, then leave the student to calculate the combined 59 mL and subtract 23 mL.
Partly supported task: change the sinker
Imagine that a different sinker displaces 31 mL rather than 23 mL. If the same block still occupies 36 mL and the starting water is 150 mL, the new sinker-only level is 181 mL and the new combined level should be 217 mL. The difference remains 217 − 181 = 36 mL. If a pupil reports the block is now 44 mL because the sinker grew by 8 mL, ask which of the two measured levels must change when the sinker changes.
Independent transfer task: unfamiliar readings
Give a fresh example without showing the earlier steps: water 200 mL; sinker only 221 mL; sinker and fully submerged mystery object 255 mL. Ask for the mystery object’s full volume. The calculation is (255 − 200) − (221 − 200) = 55 − 21 = 34 mL. A second way is 255 − 221 = 34 mL. If its dry mass is 17 g, density is 17 ÷ 34 = 0.50 g/cm³. Under the simple freshwater model, it would float with approximately half its volume submerged.
Ask the learner to explain why 21 mL is not the object’s volume, why 55 mL is not the object’s volume, and why 34 mL is. An independent explanation of all three quantities is stronger evidence of understanding than copying the correct arithmetic.
Check the measurement apparatus, not only the Mathematics
- Choose a vessel with enough capacity so the final level remains within its markings. Never extrapolate beyond the scale.
- Keep the initial volume fixed or record a new baseline whenever water is spilled or topped up.
- Use the correct meniscus reading technique for the vessel and fluid; view the scale squarely.
- Keep the sinker fully below the surface in both tests. Do not let it rest in a position that changes the measurement procedure.
- Remove air bubbles and avoid porous or absorbent materials unless investigating absorption itself.
- Repeat measurements and report a sensible precision for the graduations rather than inventing decimal places.
For a 500 mL measuring vessel marked every 5 mL, a one-millilitre-looking change cannot necessarily be resolved reliably. Use a suitable smaller-scale measuring cylinder for a small object if safe and practical. A repeat that differs by several millilitres suggests you need to inspect the method before trusting the answer.
Where learners commonly go wrong
Misconception one: ‘Floating means it has no weight.’ Incorrect: its weight is balanced by buoyancy. Misconception two: ‘Water displaced while floating equals its entire solid volume.’ It does not unless the solid is completely submerged. Misconception three: ‘The sinker only holds the object down, so I can ignore it.’ The sinker itself occupies space. Misconception four: ‘Water displacement gives volume in grams.’ Displacement measures volume; mass and density are related but not interchangeable.
A further caution: hollow objects, trapped air and water that enters a container change what ‘object volume’ should mean for the question. A boat’s external displaced envelope is not the same as the volume of its solid construction material. Define the target before taking a reading.
What pupils, parents and teachers can do next
Pupils can practise the three-column observation record with a drawing showing water level and object position. Parents can use a small sealed plastic item in a shallow tray simply to discuss why it floats; there is no need to recreate a full laboratory measurement at home. A parent can ask ‘Which number is the object’s whole size?’ and ‘What did the sinker contribute?’ and allow the child to reason before intervening.
Teachers can first assess the waterline concept, then the two-subtraction method, then independent transfer with changed values. If the child can repeat the calculation but cannot explain why the sinker trial is needed, the next lesson should return to physical modelling instead of harder arithmetic. Keep water away from electrical equipment, supervise handling and avoid improvised sharp weights.
Observable evidence of progress
A useful three-step progress record includes a labelled sketch on day one, a properly headed measurement table on day two, and a fresh calculation with an explanation a week later. Success is not a promised examination mark: it is the pupil independently identifying the full volume, explaining the subtraction and noticing a missing sinker-only reading.
Do not mistake confident speaking for accurate reasoning. A student who corrects a 59 mL answer to 36 mL after discovering what was included in the first subtraction has made visible conceptual progress.
Limitations and what the experiment cannot prove
This method assumes the object is waterproof, can be completely submerged without changing shape, and the sinker and cord are appropriately accounted for. A soggy sponge, collapsible container or swelling material violates those assumptions. A vessel that lacks sufficient graduations or has trapped bubbles will make the answer uncertain. For high-precision volume work, specialised instruments and methods may be required.
A floating displacement observation is useful in its own right when studying buoyancy. It is simply not a direct measurement of the complete volume of a partly submerged solid. The scientific habit is to keep the question, the measured quantity, and the inference aligned.
Frequently asked questions
Is one millilitre equal to one cubic centimetre?
Yes, exactly as a unit conversion: 1 mL = 1 cm³. That does not mean one millilitre of every substance has a mass of one gram. Mass per volume depends on density.
Could I calculate the block volume just from its floating displacement?
Not without additional information, such as its average density or a direct geometric measurement. Floating displacement alone primarily constrains the weight of water displaced, not the object’s complete size.
Must I use a metal sinker?
No. A suitable clean non-absorbent object that can hold the sample fully submerged and be measured separately may work. Choose safe apparatus and follow the school’s laboratory instructions.
What if the reading changes while I move the objects?
Allow the water to settle, keep the apparatus steady and repeat the trial. Record any spill or obvious trapped bubble. Do not average readings from inconsistent conditions as if they were identical measurements.
What single question checks genuine understanding?
Ask ‘Why do we subtract the sinker-only water level from the sinker-plus-block level?’ A good answer explains the physics and the unit, not merely ‘because the formula says so’.
Continue learning across eduKate
To practise related measurement judgements, compare the verified Core Aim guide to weighing small objects and the guide to fair water-temperature measurements. For specialist apparatus foundations, see Secondary 1 Chemistry measurement and accuracy. The eduKate Education learning hub develops transfer into practical decisions, and the unchanged Clementi Mathematics learning model illustrates diagnosis, explanation, guided practice and independent checking.
The bigger educational result is not the number 36. It is the moment a student can tell what a measurement really represents, identify what else entered the experiment, and design a fair way to isolate the quantity the question actually asks for.