The density formula
. Two units: and .
- : density ( or ).
- : mass ( or ).
- : volume ( or ).
Worked. A block has mass and volume .
- .
Conversion. . Water is the easy one to remember: .
- .
- Units must be consistent.
- .
- Water density: .
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Detailed notes on Motion, Forces and Energy for Cambridge IGCSE Physics, covering key concepts, explanations, examples, and exam-focused revision points.
Mass per unit volume. Use to predict whether something floats. The trickier part is measuring volume of irregular solids and reading the meniscus correctly.
Mapped to the Cambridge IGCSE 0625 syllabus (2026-2028).
. Two units: and .
Worked. A block has mass and volume .
Conversion. . Water is the easy one to remember: .
Mass on a balance, volume by geometry (regular) or displacement (irregular).
Regular solid.
Irregular solid.
Liquid.
Worked. Empty cylinder: . With liquid: .
Object floats if its density is less than the fluid's density.
Rule. An object placed in a fluid will:
Worked. A wooden block has density . Will it float in water ()?
Worked. Iron has density . In water it sinks.
Hot vs cold liquids. Heating a liquid usually decreases its density (particles spread out). That's why hot air rises, and convection currents form.
Verbatim phrases and definitions Cambridge mark schemes credit.
Density appears every Paper 2 (2-3 marks: calculate or compare densities) and most Paper 4s as part of a multi-step practical question. Examiner reports flag two errors: unit confusion ( vs ), and meniscus mis-readings on the volume.
Sources: Cambridge IGCSE Physics 0625 syllabus 2026-2028 (1.5); 0625/42 Oct/Nov 2024 — Q5 (density practical); 0625 Examiner Reports 2022-2024. Last reviewed 2026-05-06.
Step-by-step solutions to past-paper-style questions on density, written exactly the way a tutor would explain them at the board.
Almost every density exam question is one of these shapes. Learn to spot each one and you will always know how to start.
Recognise it by
Find the density (or mass) of one object, given its mass and either its dimensions or a displacement reading.
How to approach it
Find the volume first (, , or final minus initial water level), then apply — or rearrange to .
Common trap
Examiner reports flag inverting the formula to , and using a surface area instead of a volume — density is mass per unit volume, so volume needs three dimensions.
Recognise it by
Will it float? or predict / explain whether an object floats or sinks in a given fluid.
How to approach it
Compare the object's density with the fluid's density: less dense floats, denser sinks, equal means neutrally buoyant. State the comparison explicitly, then the conclusion.
Common trap
Examiner reports flag inverting the rule — an object floats only when its density is less than the fluid's, never more.
Recognise it by
Several stages chained — a unit conversion before a calculation, a missing dimension from a known density, or an average density of a combined system.
How to approach it
Do the setup step first (convert with , or find ), then add total masses over total volumes for an average density.
Common trap
Examiner reports flag forgetting the factor of in the conversion, and mixing the cavity and outer volumes when finding a hollow object's material density.
Question
A metal block has dimensions and mass . Find its density.
Step-by-step solution
Step 1
Volume.
Step 2
.
Answer
(likely iron)
Question
A stone of mass is lowered into water in a measuring cylinder; the level rises from to . Find the density.
Step-by-step solution
Step 1
Volume by displacement.
Step 2
Density.
Answer
Question
Object: density . Liquid: water (). Will it float?
Step-by-step solution
Step 1
Object density < liquid density → floats.
Answer
Yes — it floats.
Question
of mercury has density . Find the mass.
Step-by-step solution
Step 1
.
Answer
Question
A solid metal cylinder has radius , height and mass . Find its density. Take .
Step-by-step solution
Step 1
Volume of cylinder .
Step 2
Density.
Answer
Question
Aluminium has density . Convert this to SI units, and find the mass of of aluminium.
Step-by-step solution
Step 1
Use .
Step 2
in SI.
Answer
; .
Examiner tip
The examiner report flags candidates often forget the factor of in the unit conversion and quote — three orders of magnitude wrong.
Question
A block of mass has dimensions . Will it float in water () and in mercury ()?
Step-by-step solution
Step 1
Volume.
Step 2
Block density.
Step 3
Compare. In water, — the block JUST floats (neutrally buoyant). In mercury, — it floats easily.
Answer
In water: neutrally buoyant. In mercury: floats.
Question
A rectangular brass slab of density has mass and a square base of side . Find its thickness.
Step-by-step solution
Step 1
Volume from .
Step 2
Thickness from volume = base area × thickness.
Answer
Thickness
Examiner tip
The 2024 mark scheme awards method marks for explicit rearrangement of before substituting numbers.
Question
A flask contains of water () and a sealed sand bag of with volume . Find the average density of the contents.
Step-by-step solution
Step 1
Water volume.
Step 2
Total mass and volume.
Step 3
Average density.
Answer
Question
A spherical metal shell of outer radius and inner radius has mass . Find (a) the density of the metal it is made from and (b) its average density (treating the air cavity as massless). Take .
Step-by-step solution
Step 1
Outer volume.
Step 2
Inner volume.
Step 3
Volume of metal alone.
Step 4
Density of the metal.
Step 5
Average density uses outer volume.
Answer
Metal density ; average density .
Examiner tip
The examiner report flags candidates often divide total mass by total (outer) volume to get the metal's density — that mixes the two questions. Subtract the cavity volume for the material's density.
High-scoring sample answers for density on the Cambridge IGCSE 0625 paper, with examiner-style notes mapping each response to the mark scheme and assessment objectives.
Define density and state a unit in which it can be measured.
Model answer
Density is the mass per unit volume of a substance, . It can be measured in (or ).
Why this scores
One mark for 'mass per unit volume' with a correct unit. 'Mass divided by volume' is also accepted; 'how heavy something is' is not.
A metal block has a mass of and a volume of . Calculate its density.
Model answer
Why this scores
One mark for substitution into , one for with the unit. (This value suggests the block could be iron.)
A small stone has a mass of . When it is lowered into a measuring cylinder, the water level rises from to . (a) State the name of this method for finding volume. (b) Calculate the density of the stone.
Model answer
(a) The volume is found by displacement (the rise in water level equals the volume of the stone).
(b) Volume of stone . Density:
Why this scores
Three marks: naming displacement (1); volume as the difference (1); density (1). Displacement is used because the stone is an irregular shape whose volume cannot be calculated from dimensions.
A wooden block has a mass of and a volume of . (a) Calculate its density. (b) State, with a reason, whether it will float on water of density . (c) Express the block's density in .
Model answer
(a) .
(b) It floats, because its density () is less than that of water ().
(c) Using : .
Why this scores
Four marks: density (1); floats (1) because it is less dense than water (1); conversion to (1). An object floats only when it is less dense than the fluid — the comparison must be stated explicitly.
Describe an experiment to determine the density of an irregularly shaped stone. State the measurements taken, the apparatus used and how the density is calculated.
Model answer
1. Measure the mass of the stone using a balance (in grams). 2. Part-fill a measuring cylinder with water and record the initial volume reading. 3. Lower the stone in gently on a thread until it is fully submerged, and record the new volume reading. 4. The volume of the stone = final volume − initial volume (volume by displacement). 5. Calculate the density from , reading the water levels at eye level to avoid parallax error.
Why this scores
Five marks: mass with a balance (1); initial water volume (1); fully submerge the stone and read the new volume (1); volume = difference in readings (1); with a sensible precaution (1). The stone must be fully submerged and not trap air bubbles, or the volume is underestimated.
Describe how to determine the density of a liquid such as cooking oil, using a balance and a measuring cylinder. Include how the density is calculated and one precaution to improve accuracy.
Model answer
1. Place the empty, dry measuring cylinder on a balance and record its mass, . 2. Pour a measured volume of the oil into the cylinder and record the volume from the scale (read at eye level to the bottom of the meniscus to avoid parallax error). 3. Record the new total mass of the cylinder plus oil. 4. The mass of the liquid alone is — subtracting removes the mass of the container. 5. Calculate the density from . 6. To improve accuracy, use a larger volume of liquid (so any reading error is a smaller percentage of the total) and make sure the cylinder is dry inside before the first weighing.
Why this scores
Six marks: mass of empty cylinder (1); measure a known volume of liquid (1); mass of cylinder + liquid (1); liquid mass by subtraction (1); (1); a valid accuracy precaution — large volume or read the meniscus at eye level (1). Subtracting the empty-cylinder mass is the step candidates most often omit.
The formulae you need to memorise for density on the Cambridge IGCSE 0625 paper, with every variable defined in plain English and a note on when to use it.
When to use
Density problems for any homogeneous substance.
When to use
Switching between and .
Definitions to memorise and the exact keywords mark schemes credit for density answers — sharpened from recent examiner reports for the 2026 0625 sitting.
Mass per unit volume of a substance.
Volume of an irregular object found from the rise in water level when fully submerged.
The traps other students keep falling into on density questions — taken from recent Cambridge IGCSE 0625 examiner reports and mark schemes — and how to avoid them.
0625/42 — recurring
Why it happens
Different question parts use different units.
How to avoid it
Convert: .
Why it happens
Mixing up cm² and cm³.
How to avoid it
Volume of a cuboid is — three dimensions.
Why it happens
Misremembering which is on top.
How to avoid it
Density is mass PER unit volume — so mass on top.
Why it happens
Inverting the rule.
How to avoid it
Floats only if object density is LESS than fluid density.
The things students keep getting wrong in this sub-topic, answered.
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