ScienceCBSE Class 8 · The Amazing World of Solutes, Solvents, and Solutions

Density, Mass, Volume and Floating: Class 8 Science

Updated 17 October 2026 · Fact-checked

Density is the mass present in a unit volume of a substance: density = mass ÷ volume. Its SI unit is kg/m3 (g/cm3 and g/mL are also used). Relative density is the density of a substance divided by the density of water. Mass is measured with a balance and volume with a measuring cylinder (displacement for irregular solids). Density generally falls on heating, and an object denser than water generally sinks.

Divide mass by volume to get density; an object less dense than water (1 g/cm³) floats, and a denser one sinks.

Illustration drawn for QuestionBuddy.

Understand Density, Measuring Mass and Volume, and Floating

Why density. Wood and iron of the same size feel different because they have different densities. Density is the mass present in a unit volume of a substance: Density = Mass ÷ Volume. It does not depend on the shape or size of the sample but does depend on temperature and pressure (pressure mainly matters for gases).

Units. The SI unit is kg/m3; for liquids g/mL and g/cm3 are convenient. The chapter gives the conversion 1 kg/m3 = 1000 g per 1000 L = 1 g/L = 1 g per 1000 mL = 1 g per 1000 cm3. The mass of 1 mL of water is close to 1 g at room temperature, so 10 mL of water is about 10 g. Example from the chapter: an aluminium block of mass 27 g and volume 10 cm3 has density 2.7 g/cm3, so it is 2.7 times denser than water; its relative density with respect to water is 2.7 (no unit), where relative density = density of the substance ÷ density of water at that temperature.

Measuring mass (Activity 9.3). Use a balance. For a digital balance, switch on, check zero (press tare), place a clean watch glass, tare again, then place the object (or use a beaker for a liquid). Most balances actually measure weight but are marked in mass units; the exception is the two-pan balance.

Measuring volume. Units: m3 (SI), dm3 or cm3 (cc); litre (L) equals 1 dm3; mL equals 1 cm3. A measuring cylinder is narrow and tall; the smallest reading is found by dividing the value between two big marks by the number of small divisions. In the 100 mL cylinder (Fig. 9.16): 10 mL between big marks divided by 10 divisions gives 1 mL. Typical smallest readings: 0.1 mL for 10 mL or 25 mL cylinders, 1 mL for 100 mL, 2 mL for 250 mL, 5 mL for 500 mL. To measure 70 mL a 100 mL cylinder is best: a 50 mL one needs two steps, and a larger one is less accurate. Read the bottom of the meniscus with the eye level with it (for coloured liquids, the top of the meniscus).

Regular solid: volume = length x width x height (notebook 25 cm x 18 cm x 2 cm = 900 cm3).
Irregular solid: displacement. Lower a stone tied with a thread into water in a measuring cylinder; the rise in level (final minus initial) is its volume. Example: 50 mL to 55 mL gives 5 cm3. With mass 16.400 g its density is 16.400 ÷ 5 = 3.28 g/cm3.

Effect of temperature and pressure. On heating, particles move apart, the volume increases and the mass stays the same, so density decreases. That is why hot air rises and hot air balloons work. In gases, higher pressure forces particles closer, reducing volume and increasing density. Liquids are nearly incompressible; solids even less, so their density changes little.

Floating and sinking. Objects lighter (less dense) than the liquid tend to float and denser ones sink: sawdust floats and sand sinks in water; oil floats on water; rice sinks while husk floats. Some results look unexpected but are still explained by the density of the whole object. Pumice and bamboo float; an orange floats unpeeled because air trapped in the peel lowers its average density, and it sinks when peeled (an exercise). Ice floats because water's density is highest at 4 degrees Celsius and on freezing at 0 degrees Celsius its particles arrange to take more space, so ice is less dense; the floating ice layer keeps the water below warm enough for aquatic life.

The previous topic covers solutions.

Density, Measuring Mass and Volume, and Floating: formulas and key facts

Density: $D e n s i t y = M a ss / V o l u m e$; SI unit kg/m3; also g/cm3 and g/mL.
Relative density: $R e l a t i v e d e n s i t y = D e n s i t y o f s u b s t an ce / D e n s i t y o f w a t er$; No unit. Water is about 1 g/cm3.
Volume of a cuboid: $V = l \times w \times h$; Use cm for cm3.
Volume by displacement: $V = F ina l l e v e l - I ni t ia l l e v e l$; In mL, equal to cm3 for solids.
Smallest reading of a measuring cylinder: (Value between two big marks) / (Number of small divisions); Chapter example: 10 mL / 10 = 1 mL.
Effect of temperature: Heating: volume up, mass same, density down; Hot air is less dense and rises.

How to solve Density, Measuring Mass and Volume, and Floating questions

Use this method for density numericals.

1Write mass and volume with units; convert so that they match (g and cm3, or kg and m3).
2If the volume is not given, find it: cuboid by l × w × h, irregular solid by displacement.
3Write density = mass ÷ volume and substitute.
4Give the unit (g/cm3 or kg/m3).
5Compare with water (1 g/cm3): greater density suggests sinking, smaller suggests floating.
6For relative density, divide by the density of water at that temperature.

Density, Measuring Mass and Volume, and Floating in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Is the ghee pack lighter than water

Suppose a pack says 1 litre of cooking oil has a mass of 910 g, and another oil is 500 mL with mass 455 g (an invented pack in the style of the chapter's example).

(a) Find the density of the first oil in g/mL. (b) Find the density of the second. (c) Will they float on water? (d) How much does 2 L of the first oil weigh in kg?

Try it first, then show the solutionSolution

1 L = 1000 mL; 910 ÷ 1000 = 0.91 g/mL.
455 ÷ 500 = 0.91 g/mL.
Both are less dense than water (1 g/mL), so they float.
2 L = 2000 mL; mass = 2000 × 0.91 = 1820 g = 1.82 kg.

Answer: (a) 0.91 g/mL; (b) 0.91 g/mL; (c) yes; (d) 1.82 kg.

Memory hook: Density does not depend on how much you take.

Hot air rises

Imagine 1.2 kg of room air occupies 1 m3, and when the same mass is warmed in a balloon it expands to 1.5 m3 (invented values).

(a) Find the density before and after. (b) Find the percentage decrease. (c) Explain why the balloon rises.

Try it first, then show the solutionSolution

Before: 1.2 ÷ 1 = 1.2 kg/m3. After: 1.2 ÷ 1.5 = 0.8 kg/m3.
(1.2 − 0.8) ÷ 1.2 × 100 = 33.3%.
The warm air is less dense than the cooler air around it, so it moves up.

Answer: (a) 1.2 and 0.8 kg/m3; (b) 33.3%; (c) hot air is less dense.

Memory hook: Heat spreads particles, so the same mass fills more space.

Tricks to remember Density, Measuring Mass and Volume, and Floating

Short memory aids. Say each one aloud once, then use it on a question the same day.

M over V
Density = Mass over Volume; mass sits on the roof, volume at the base.
Use it when: Formula recall.
Water is 1
Water is 1 g/cm3, so relative density is just the density in g/cm3.
Use it when: Float or sink check.
Displacement = rise
Stone volume = final minus start.
Use it when: Irregular solids.
Bottom of the bowl
Read the bottom of the meniscus with eyes level.
Use it when: Reading the cylinder.

Density, Measuring Mass and Volume, and Floating: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: A direct density calculation · 2 marks · Short answerBoard level

A block of metal has a mass of 156 g and a volume of 20 cm3. Find its density in g/cm3 and its relative density.

Try it first, then show the solutionSolution

Density = 156 g ÷ 20 cm3 = 7.8 g/cm3. (1)
Relative density = 7.8 ÷ 1 = 7.8 (no unit). (1)

Answer: 7.8 g/cm3; relative density 7.8

Example 2: Smallest reading of a cylinder · 1 mark · MCQBoard level

On a 50 mL measuring cylinder, the gap between big marks is 10 mL and there are 20 small divisions between them. The smallest volume it can read is
(a) 0.2 mL
(b) 0.5 mL
(c) 1 mL
(d) 2 mL

Try it first, then show the solutionSolution

10 mL ÷ 20 = 0.5 mL.

Answer: (b)

Example 3: Density of an irregular stone · 5 marks · Long answerHarder board level

A stone tied with a thread is lowered into a measuring cylinder holding 60 mL of water. The level rises to 78 mL. The mass of the stone is 49.5 g.
(a) Find the volume of the stone. (1)
(b) Find its density in g/cm3. (1)
(c) Express the density in kg/m3. (1)
(d) Find its relative density and say if it sinks in water. (2)

Try it first, then show the solutionSolution

(a) 78 − 60 = 18 mL = 18 cm3. (1)
(b) 49.5 ÷ 18 = 2.75 g/cm3. (1)
(c) 2.75 g/cm3 = 2.75 g/mL = 2750 g/L = 2750 kg/m3 using 1 g/L = 1 kg/m3. (1)
(d) Relative density = 2.75 ÷ 1 = 2.75; it is denser than water and sinks. (2)

Answer: (a) 18 cm3; (b) 2.75 g/cm3; (c) 2750 kg/m3; (d) 2.75, sinks.

Example 4: Heating a liquid · 4 marks · Case-basedHarder board level

Read the passage and answer.

2000 mL of a liquid at 20 degrees Celsius has a mass of 1800 g. On heating, it expands to 2100 mL without losing any liquid.
(a) Find the density before heating. (1)
(b) Find the density after heating, to three decimal places. (1)
(c) Find the percentage decrease in density, to one decimal place. (1)
(d) Explain why the density decreased although the mass did not change. (1)

Try it first, then show the solutionSolution

(a) 1800 ÷ 2000 = 0.9 g/mL. (1)
(b) 1800 ÷ 2100 = 0.857 g/mL. (1)
(c) Decrease = 0.9 − 0.857 = 0.043 g/mL; 0.043 ÷ 0.9 × 100 ≈ 4.8%. Check: 1 − 2000/2100 = 100/2100 = 4.76%, about 4.8%. (1)
(d) Heating moves particles apart, so the volume increases while the mass stays the same, so density = mass ÷ volume decreases. (1)

Answer: (a) 0.9 g/mL; (b) 0.857 g/mL; (c) about 4.8%; (d) volume increased, mass the same.

Example 5: Which floats · 4 marks · Case-basedHOTS / competency

Read the passage and answer.

Object P has mass 150 g and volume 50 cm3. Object Q has mass 90 g and volume 100 cm3. Both are solid and uniform. Water has density 1 g/cm3. A student says P floats because it is heavier in mass than Q.
(a) Find the densities of P and Q. (1)
(b) Predict which floats and which sinks in water. (1)
(c) Why is the student's reasoning wrong? (1)
(d) Give one example from the chapter where an object's floating or sinking seems unexpected, and explain it using density. (1)

Try it first, then show the solutionSolution

(a) P: 150 ÷ 50 = 3 g/cm3. Q: 90 ÷ 100 = 0.9 g/cm3. (1)
(b) P is denser than water and sinks; Q is less dense and floats. (1)
(c) Floating depends on density (mass per volume), not on mass alone. (1)
(d) An unpeeled orange floats because air trapped in its peel lowers its average density below that of water; a peeled orange sinks because its density is greater than that of water. (1)

Answer: (a) 3 g/cm3 and 0.9 g/cm3; (b) P sinks, Q floats; (c) mass alone does not decide; (d) an unpeeled orange floats (trapped air lowers its average density) and a peeled orange sinks (denser than water).

Where students lose marks in Density, Measuring Mass and Volume, and Floating

The slips examiners see most often, and what to write instead.

Mistake: Using mL for a solid's volume without converting to cm3 label.
Units differ for liquids and solids.
Wrong working
Density = 54 g ÷ 20 mL = 2.7 g/mL (for a stone, no explanation).
Right working
The volume of the stone is 20 mL = 20 cm3, so the density is 2.7 g/cm3.
Do this: Write the equivalent unit for solids.
Usually costs: ½ mark.
Mistake: Forgetting to subtract the initial level.
Only the final reading is noted.
Wrong working
Volume of stone = 78 cm3
Right working
Volume = 78 − 60 = 18 cm3
Do this: Always compute final minus initial.
Usually costs: 2 marks.
Mistake: Saying a heavy object always sinks.
Mass is confused with density.
Wrong working
A 5 kg wooden log sinks because it has more mass than a 1 g coin.
Right working
Compare densities, not masses: the log is less dense than water.
Do this: Use mass per unit volume.
Usually costs: 1 mark.
Mistake: Reading the meniscus from the top for water.
Eye position and mark are ignored.
Wrong working
Read the top edge of the curve for water.
Right working
For water and colourless liquids read the bottom of the meniscus with eyes level; for coloured liquids use the top.
Do this: Learn the rule.
Usually costs: ½ mark.

Exam tips

Write density, mass and volume with units in every step.
Convert mL to cm3 for solids and quote the SI unit when asked.
Use water as 1 g/cm3 to decide floating or sinking.
State what stays constant on heating (mass) and what changes (volume, density).
Show the displacement subtraction explicitly.

Practice questions on Density, Measuring Mass and Volume, and Floating

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 2 marks · Very short answerBoard level
Define density and give its SI unit.
Hint
Mass in a unit volume.
Answer
Density is the mass present in a unit volume of a substance (1); the SI unit is kg/m3 (1).
Q2 · 1 mark · MCQBoard level
Which of the following will NOT change the density of a piece of iron?
(a) Heating it a lot
(b) Cutting it into two equal pieces
(c) Cooling it a lot
(d) Warming it from 20 to 60 degrees Celsius
Hint
Density does not depend on size.
Answer
(b)
Q3 · 1 mark · Assertion-reasonHarder board level
Assertion (A): Ice floats on water.
Reason (R): On freezing, water particles arrange so that the same mass occupies more space, so ice is less dense than water.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Hint
Lower density means floating.
Answer
(a) R explains A.
Q4 · 4 marks · Short answerHarder board level
A stone of mass 54 g is lowered into a measuring cylinder with 40 mL of water and the level rises to 60 mL. (a) Find the volume of the stone. (b) Find its density in g/cm3. (c) Express it in kg/m3. (d) Will it float in water? Give the relative density.
Hint
60 − 40 = 20 mL.
Answer
(a) 20 cm3. (b) 54 ÷ 20 = 2.7 g/cm3. (c) 2700 kg/m3. (d) Relative density 2.7; it sinks (1 mark each).
Q5 · 4 marks · Case-basedHOTS / competency
Read the passage and answer.
A 100 mL cylinder is used to measure 70 mL of water, then a coloured liquid is read by another student who looks from above the mark. A cuboid block measures 8 cm x 5 cm x 2.5 cm and has a mass of 120 g.
(a) Why is a 100 mL cylinder preferred for 70 mL? (b) Find the block's volume. (c) Find its density. (d) Does the block float on water?
Hint
8 × 5 × 2.5 = 100 cm3.
Answer
(a) A 50 mL cylinder needs two steps and a 250 or 500 mL one has a larger smallest reading, so 100 mL is best. (b) 8 × 5 × 2.5 = 100 cm3. (c) 120 ÷ 100 = 1.2 g/cm3. (d) No; its density is above that of water, so it sinks (1 mark each).

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.What is the formula for density?Show answer
Density = mass ÷ volume.
2.What is relative density?Show answer
Density of a substance divided by the density of water; it has no unit.
3.At which temperature is the density of water highest?Show answer
4 degrees Celsius.
4.How is the volume of an irregular solid found?Show answer
By displacement of water in a measuring cylinder.
5.Why does a hot air balloon rise?Show answer
Hot air is less dense than the cooler air around it.

Density, Measuring Mass and Volume, and Floating: frequently asked questions

Does density depend on the size of the sample?

No. The density of a substance is independent of its shape or size, but it depends on temperature and pressure.

Why is a measuring cylinder narrow and tall?

The chapter poses this as a question; a narrow cylinder gives a larger change in level for a small volume change, so the scale can be read more precisely (an explanation derived here, not printed in the chapter).

Do balances measure mass or weight?

Most balances measure weight but are marked in mass units; a two-pan balance compares masses.

Does pressure change the density of solids?

Solids are even less affected than liquids, so the change is usually negligible.