S2 Science: Density And Floating (Paper 3 (challenge))

S2 Science: Density and Floating (Paper 3 (challenge))

2026-11-14

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Tutor Prep Guide · Probability scale, favourable over total outcomes, comparing and expected counts

S2 Science: Density and Floating (Paper 3 (challenge))

This paper is the challenge: particle gaps, alloy and overflow densities, the exposed fraction of a floating block, and hollow ball checks.

Direct answers　For mixtures and hollow bodies, find the total mass and total volume first, then divide; never add densities. The particle model has three ideas: particles have volume, gaps lie between them, and they move constantly.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	20
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: S2 Science: Density and Floating
Level	S2

02　Questions (10 items)

FoundationMixing 100 cm³ of water with 100 cm³ of alcohol gives less than 200 cm³. How does the particle model explain this?
FoundationA 50 g metal of volume 10 cm³ is melted with 60 g of another metal of volume 20 cm³. Find the alloy density.
FoundationAn object of mass 87 g is lowered into a brim-full displacement can and 30 cm³ of water overflows. Find its density and whether it floats.
IntermediateA block of density 0.6 g/cm³ and volume 500 cm³ floats. What volume shows above the water?
IntermediateA floating ice cube melts completely. Does the water level rise, fall or stay the same?
IntermediateA liquid of density 1.2 g/cm³ is measured out at 250 cm³. What is its mass?
ChallengeA ball has an outer volume of 40 cm³ and a mass of 100 g. Find the average density and say whether it is hollow if made of iron at 7.9 g/cm³.
ChallengeOil has a density of 0.9 g/cm³. What is that in kg/m³?
ChallengeHow many cm³ are there in 1 m³?
Error redoA student adds the volumes of 100 cm³ of water and 100 cm³ of alcohol to get 200 cm³. What is wrong?

03　Answers and one-line notes

#	Answer	One-line note
1	The two kinds of particles differ in size and slip into the gaps between each other	Particles have gaps between them, and mixing fills some of those gaps, so the total shrinks a little.
2	About 3.67 g/cm³	Total mass is 110 g over a total volume of 30 cm³, giving about 3.67 g/cm³.
3	2.9 g/cm³, so it sinks	The overflow equals the object volume, and 87 divided by 30 is 2.9, denser than water.
4	200 cm³, which is 40%	The submerged part is 0.6 of the block, that is 300 cm³, so 200 cm³ shows above.
5	It stays the same	The floating ice displaces water equal to its own weight, and the melt water exactly fills that space.
6	300 g	1.2 times 250 is 300 g, two tenths heavier than the same volume of water.
7	2.5 g/cm³, so it is hollow	100 divided by 40 is 2.5, far below 7.9, so the inside must be empty.
8	900 kg/m³	Since 1 g/cm³ is 1 000 kg/m³, 0.9 gives 900 kg/m³.
9	1 000 000 cm³	One metre is 100 cm, and 100 cubed is 1 000 000, so a cubic metre of water is 1 000 kg.
10	The particles fill each other gaps, so the total is slightly less than 200 cm³	Volumes can only be added for one substance; mixed liquids must be measured, not summed.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

There is one density formula: density equals mass divided by volume; to judge floating, compare the object density with the liquid density.Tutor Registration →

Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.