PhysicsICSE Class 8 · Physical Quantities and Measurement

Density: ρ = m/V, Units and Numericals (ICSE Class 8 Physics)

Updated 17 October 2026 · Fact-checked

Density is mass per unit volume, ρ = m/V. Its SI unit is kg/m³, and 1 g/cm³ = 1000 kg/m³. Water has a density of about 1 g/cm³ (1000 kg/m³). Density does not depend on the amount of the substance.

Same volume, more mass means higher density: iron is denser than wood. Cover one letter of the triangle to get the formula, and ×1000 turns g/cm³ into kg/m³.

Illustration drawn for QuestionBuddy.

Understand Density and Density Numericals

Density is the mass of a unit volume of a substance:

$ρ = \frac{m}{V}$ , so $m = ρ V$ and $V = \frac{m}{ρ}$ .

Units.

SI unit: kg/m³; practical unit: g/cm³.
$1 g/cm^{3} = 1000 kg/m^{3}$ : multiply by 1000 to go from g/cm³ to kg/m³, divide by 1000 to come back.
$1 mL = 1 cm^{3}$ ; $1 L = 1000 cm^{3}$ ; $1 m^{3} = 1 0^{6} cm^{3}$ .
Pure water: about $1 g/cm^{3}$ or $1000 kg/m^{3}$ .

Meaning. Iron has more mass in the same volume than wood, so iron is denser. Density is a property of the material: a small and a large piece of the same pure metal have the same density.

Volume of regular solids. Cuboid: $l \times b \times h$ ; cube: $a^{3}$ . Convert to the unit you need before dividing.

Mixtures of liquids (assuming the volumes add):
$ρ_{mixture} = \frac{m _{1} + m _{2}}{V _{1} + V _{2}}$ , where $m_{1} = ρ_{1} V_{1}$ and $m_{2} = ρ_{2} V_{2}$ .

Density in the three states. For the same substance, $solid > liquid ≫ gas$ . Air is about $1.3 kg/m^{3}$ . Water is an exception: ice (about $0.92 g/cm^{3}$ ) is less dense than liquid water, so ice floats.

Floating and sinking. An object less dense than the liquid floats; a denser one sinks. (Details on the next topic page.)

Density and Density Numericals: formulas and key facts

Density: $ρ = \frac{m}{V}$; Also m = ρV, V = m/ρ.
Unit conversion: $1 g/cm^{3} = 1000 kg/m^{3}$; Water is 1 g/cm³ = 1000 kg/m³.
Mixture of liquids: $ρ = \frac{ρ _{1} V _{1} + ρ _{2} V _{2}}{V _{1} + V _{2}}$; Volumes assumed to add.
Volume units: $1 mL = 1 cm^{3} 1 m^{3} = 1 0^{6} cm^{3}$; 1 L = 1000 cm³.

How to solve Density and Density Numericals questions

Keep mass and volume in matching units, then apply the formula.

1Choose one system: g with cm³ (answer in g/cm³) or kg with m³ (answer in kg/m³).
2Find the volume if it is not given (length × breadth × height).
3Use $ρ = \frac{m}{V}$ or its rearrangement.
4Convert the answer if the question wants the other unit.
5For a mixture, add the masses and add the volumes first.

Density and Density Numericals 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.

Oil on water

Suppose cooking oil of mass 80 g fills 100 cm³ in a measuring cylinder, and you pour it gently on to water.

Find the density of the oil in g/cm³ and kg/m³, and say what you will see.

Try it first, then show the solutionSolution

$ρ = \frac{80}{100} = 0.8$ g/cm³.
In SI: $0.8 \times 1000 = 800$ kg/m³.
It is less dense than water (1 g/cm³), so it floats.

Answer: 0.8 g/cm³ or 800 kg/m³; the oil floats on water.

Memory hook: Less dense floats.

Air in a classroom

Imagine a classroom of size 8 m by 6 m by 3 m, with air of density 1.3 kg/m³.

Find the mass of air in the room.

Try it first, then show the solutionSolution

$V = 8 \times 6 \times 3 = 144$ m³.
$m = ρ V = 1.3 \times 144 = 187.2$ kg.

Answer: 187.2 kg, about the mass of several students.

Memory hook: Even air has mass.

Tricks to remember Density and Density Numericals

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

M over V
ρ = m ÷ V: "density is mass squeezed into each unit of volume".
Use it when: Formula.
×1000 for SI
g/cm³ to kg/m³: multiply by 1000; back: divide by 1000.
Use it when: Units.
Triangle
Cover m for ρ × V; cover V for m ÷ ρ; cover ρ for m ÷ V.
Use it when: Rearranging.

Density and Density Numericals: solved examples

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

Example 1: Compute the density · 1 mark · MCQBoard level

A solid has a mass of 200 g and a volume of 50 cm³. Its density is:
(a) 0.25 g/cm³
(b) 4 g/cm³
(c) 250 g/cm³
(d) 10 g/cm³

Try it first, then show the solutionSolution

$ρ = \frac{200}{50} = 4$ g/cm³.

Answer: (b) 4 g/cm³

Example 2: Unit change · 2 marks · Short answerBoard level

Express a density of 2.7 g/cm³ in kg/m³. Show the working.

Try it first, then show the solutionSolution

$2.7 g/cm^{3} \times 1000$ . (1)
$= 2700$ kg/m³. (1)

Answer: 2700 kg/m³

Example 3: Density of a block · 4 marks · Long answerHarder board level

A rectangular block measures 5 cm × 4 cm × 2.5 cm and has mass 135 g. Find (a) its volume, (b) its density in g/cm³, (c) its density in kg/m³, (d) the mass of 0.002 m³ of the same material.

Try it first, then show the solutionSolution

(a) $V = 5 \times 4 \times 2.5 = 50$ cm³. (1)
(b) $ρ = \frac{135}{50} = 2.7$ g/cm³. (1)
(c) $2.7 \times 1000 = 2700$ kg/m³. (1)
(d) $m = 2700 \times 0.002 = 5.4$ kg. (1)

Answer: (a) 50 cm³ (b) 2.7 g/cm³ (c) 2700 kg/m³ (d) 5.4 kg

Example 4: Oil and water · 3 marks · Short answerHarder board level

100 mL of oil of density 0.8 g/cm³ is mixed with 100 mL of water (1 g/cm³). Assuming the volumes add, find (a) the mass of each, (b) the density of the mixture.

Try it first, then show the solutionSolution

(a) Oil: $0.8 \times 100 = 80$ g; water: $1 \times 100 = 100$ g. (1)
(b) Total mass $= 180$ g, total volume $= 200$ cm³. (1)
$ρ = \frac{180}{200} = 0.9$ g/cm³. (1)

Answer: (a) 80 g and 100 g (b) 0.9 g/cm³

Example 5: Are they the same material? · 4 marks · Case-basedHOTS / competency

Cube A has side 4 cm and mass 192 g; cube B has side 3 cm and mass 108 g. (a) Find the density of each. (b) Can they be made of the same material? (c) What would be the mass of a 5 cm cube of A?

Try it first, then show the solutionSolution

(a) $V_{A} = 64$ cm³, $ρ_{A} = \frac{192}{64} = 3$ g/cm³; $V_{B} = 27$ cm³, $ρ_{B} = \frac{108}{27} = 4$ g/cm³. (2)
(b) No, densities differ, and density is a property of the material. (1)
(c) $V = 125$ cm³; $m = 3 \times 125 = 375$ g. (1)

Answer: (a) 3 g/cm³ and 4 g/cm³ (b) no (c) 375 g

Where students lose marks in Density and Density Numericals

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

Mistake: Mixed units
g with m³ give wrong answers.
Wrong working
$ρ = \frac{200 g}{0.00005 m ^{3}}$ called kg/m³.
Right working
Use 200 g and 50 cm³ for g/cm³, or 0.2 kg and 0.00005 m³ for kg/m³.
Do this: Match mass and volume units.
Mistake: Averaging densities in a mixture
The mixture density is total mass over total volume.
Wrong working
$\frac{0.8 + 1.0}{2} = 0.9$ with unequal volumes.
Right working
$\frac{ρ _{1} V _{1} + ρ _{2} V _{2}}{V _{1} + V _{2}}$ .
Do this: Find masses and volumes before dividing.
Mistake: Wrong conversion factor
1 g/cm³ = 1000 kg/m³.
Wrong working
"2.7 g/cm³ = 27 kg/m³."
Right working
"2.7 g/cm³ = 2700 kg/m³."
Do this: Multiply by 1000.

Exam tips

Write ρ = m/V, substitute with units and give the unit of the answer.
Show every conversion as a separate line.
For mixtures state your assumption (volumes add).
Check: water is 1 g/cm³ or 1000 kg/m³.

Practice questions on Density and Density Numericals

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

Q1 · 1 mark · Very short answerBoard level
Find the volume of 0.5 kg of a liquid whose density is 800 kg/m³ in m³ and in cm³.
Hint
$V = \frac{m}{ρ}$ .
Answer
$V = \frac{0.5}{800} = 0.000625$ m³ $= 625$ cm³.
Q2 · 2 marks · Short answerHarder board level
The density of air is 1.3 kg/m³. Find the mass of air in a room of size 5 m × 4 m × 3 m.
Hint
Find the volume first.
Answer
$V = 60$ m³; $m = 1.3 \times 60 = 78$ kg.
Q3 · 3 marks · Short answerHarder board level
An ornament weighs 0.27 kg on a balance and is made of a material of density 2700 kg/m³. Find its volume in m³ and in cm³. Would it float in water?
Hint
Use SI units, then compare with water.
Answer
$V = \frac{0.27}{2700} = 0.0001$ m³ $= 100$ cm³. Its density (2700 kg/m³) is greater than that of water (1000 kg/m³), so it sinks.
Q4 · 3 marks · Short answerHarder board level
A metal cylinder of radius 7 cm and height 10 cm has density 3 g/cm³. Find its volume (use π = 22/7) and mass.
Hint
$V = π r^{2} h$ .
Answer
$V = \frac{22}{7} \times 49 \times 10 = 1540$ cm³; $m = 3 \times 1540 = 4620$ g $= 4.62$ kg.
Q5 · 4 marks · Long answerHOTS / competency
300 cm³ of liquid A (density 1.2 g/cm³) is mixed with 200 cm³ of liquid B (density 0.8 g/cm³). Assume the volumes add. Find the density of the mixture, and say whether a small body of density 1.0 g/cm³ would float or sink in it.
Hint
Add masses and volumes.
Answer
$m_{A} = 360$ g; $m_{B} = 160$ g; total $= 520$ g; $V = 500$ cm³; $ρ = \frac{520}{500} = 1.04$ g/cm³. The body (1.0) is less dense than the mixture, so it floats.

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.SI unit of density?Show answer
kg/m³.
2.1 g/cm³ in kg/m³?Show answer
1000 kg/m³.
3.Density of water?Show answer
1 g/cm³.
4.Formula for mass from density?Show answer
m = ρV.
5.Does density depend on the amount?Show answer
No.

Density and Density Numericals: frequently asked questions

What is density?

Density is the mass per unit volume of a substance, ρ = m/V. Its SI unit is kg/m³.

How do you convert g/cm³ to kg/m³?

Multiply by 1000: 1 g/cm³ = 1000 kg/m³.

How do you find the density of a mixture of two liquids?

Add the masses (density × volume of each) and the volumes, then divide total mass by total volume, assuming the volumes add.