IGCSE Physics Density: Complete Guide for Cambridge IGCSE Physics (0625)

Density is a fundamental concept in Cambridge IGCSE Physics (0625) that describes how much matter is packed into a given space. Understanding the density formula, learning to calculate density, and mastering techniques for measuring density are essential skills for achieving top grades in your IGCSE Physics exams.

This comprehensive IGCSE Physics Density guide covers everything you need to know, including the density formula, calculating density for regular and irregular objects, measuring density for liquids, the displacement method, step-by-step worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE Physics tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to calculate density, measure density for different objects and liquids, use the displacement method, and apply these skills confidently in IGCSE Physics exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Physics Density practice deck featuring exam-style questions, videos, and instant feedback.

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Why Density Matters in IGCSE Physics

Density is a crucial topic that appears throughout the IGCSE Physics syllabus. Here’s why it’s so important:

• High exam frequency: Density questions appear in almost every IGCSE Physics paper
• Exam weight: Typically worth 6-10 marks per paper, making it crucial for grade boundaries
• Practical skills: Develops essential laboratory measurement techniques
• Foundation for advanced topics: Essential for understanding floating, sinking, pressure, and material properties
• Real-world applications: Used in material science, engineering, quality control, and everyday life
• Common confusion: Students often struggle with units and volume calculations

Key insight from examiners: Students often lose marks not because they don’t understand density, but because they make errors in unit conversions, volume calculations, or measurement techniques. This guide will help you avoid these pitfalls.

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What is Density?

Density is the mass per unit volume of a substance. It tells us how much matter is packed into a given space.

Understanding Density

Key concept:

• Density describes how “packed” or “compact” a material is
• A dense material has a lot of mass in a small volume
• A less dense material has less mass in the same volume

Examples:

• Lead is very dense - a small piece is very heavy
• Styrofoam is not dense - a large piece is very light
• Water has a density of 1000 kg/m³ (or 1 g/cm³)

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The Density Formula

The relationship between density, mass, and volume is given by:

Density Formula:

Density = Mass ÷ Volume

Or using symbols:

ρ = m ÷ V

Where:

• ρ (rho) = density (in kg/m³ or g/cm³)
• m = mass (in kg or g)
• V = volume (in m³ or cm³)

Rearranging the Formula

You can rearrange this formula to find any of the three quantities:

To find density:

ρ = m ÷ V

To find mass:

m = ρ × V

To find volume:

V = m ÷ ρ

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Units of Density

Density can be expressed in different units depending on the units used for mass and volume:

Common Density Units

Mass Unit	Volume Unit	Density Unit	Example
kg	m³	kg/m³	1000 kg/m³ (water)
g	cm³	g/cm³	1.0 g/cm³ (water)
kg	cm³	kg/cm³	(rarely used)

Most common units in IGCSE Physics:

• kg/m³ (kilograms per cubic metre)
• g/cm³ (grams per cubic centimetre)

Converting Between Density Units

Converting g/cm³ to kg/m³:

• Multiply by 1000
• Example: 1 g/cm³ = 1 × 1000 = 1000 kg/m³

Converting kg/m³ to g/cm³:

• Divide by 1000
• Example: 1000 kg/m³ = 1000 ÷ 1000 = 1 g/cm³

Memory tip:

• To convert g/cm³ → kg/m³: multiply by 1000 (getting bigger)
• To convert kg/m³ → g/cm³: divide by 1000 (getting smaller)

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Worked Example 1: Calculating Density of a Regular Object

A metal block has a mass of 540 g and dimensions of 10 cm × 5 cm × 3 cm. Calculate its density in g/cm³.

Solution:

Step 1: Calculate the volume

• Volume = length × width × height
• Volume = 10 cm × 5 cm × 3 cm
• Volume = 150 cm³

Step 2: Identify known values

• Mass (m) = 540 g
• Volume (V) = 150 cm³

Step 3: Use the density formula

• ρ = m ÷ V
• ρ = 540 ÷ 150
• ρ = 3.6 g/cm³

Answer: The density of the metal block is 3.6 g/cm³.

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Worked Example 2: Density with Unit Conversion

A paving slab has a mass of 73 kg and dimensions 0.04 m × 0.5 m × 0.85 m. Calculate the density, in kg/m³, of the material from which the paving slab is made.

Solution:

Step 1: Calculate the volume

• Volume = length × width × height
• Volume = 0.04 m × 0.5 m × 0.85 m
• Volume = 0.017 m³

Step 2: Identify known values

• Mass (m) = 73 kg
• Volume (V) = 0.017 m³

Step 3: Use the density formula

• ρ = m ÷ V
• ρ = 73 ÷ 0.017
• ρ = 4294.12… kg/m³

Step 4: Round to appropriate significant figures

• ρ = 4300 kg/m³ (to 2 significant figures)

Answer: The density of the paving slab material is 4300 kg/m³.

Examiner tip: Always check the required precision and round your answer appropriately.

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Volume Formulas for Common Shapes

To calculate density, you often need to find the volume first. Here are the volume formulas for common shapes:

Volume of a Cube

Volume = side³

Or:

V = s³

Example: A cube with side length 5 cm
Volume = 5³ = 5 × 5 × 5 = 125 cm³

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Volume of a Rectangular Prism (Cuboid)

Volume = length × width × height

Or:

V = l × w × h

Example: A box with length 10 cm, width 5 cm, height 3 cm
Volume = 10 × 5 × 3 = 150 cm³

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Volume of a Cylinder

Volume = π × radius² × height

Or:

V = π × r² × h

Where π ≈ 3.14 (or use calculator value)

Example: A cylinder with radius 4 cm, height 10 cm
Volume = π × 4² × 10 = π × 16 × 10 = 502.7 cm³ (1 d.p.)

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Volume of a Sphere

Volume = (4/3) × π × radius³

Or:

V = (4/3) × π × r³

Example: A sphere with radius 5 cm
Volume = (4/3) × π × 5³ = (4/3) × π × 125 = 523.6 cm³ (1 d.p.)

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Worked Example 3: Density of a Cylinder

A cylindrical metal rod has a radius of 2 cm, a height of 10 cm, and a mass of 490 g. Calculate its density in g/cm³. (Take π = 3.14)

Solution:

Step 1: Calculate the volume of the cylinder

• Volume = π × r² × h
• Volume = 3.14 × (2)² × 10
• Volume = 3.14 × 4 × 10
• Volume = 125.6 cm³

Step 2: Identify known values

• Mass (m) = 490 g
• Volume (V) = 125.6 cm³

Step 3: Use the density formula

• ρ = m ÷ V
• ρ = 490 ÷ 125.6
• ρ = 3.9 g/cm³ (to 2 significant figures)

Answer: The density of the metal rod is 3.9 g/cm³.

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Measuring Density: Methods and Techniques

The method for measuring density depends on whether you have a regular solid, irregular solid, or liquid.

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Method 1: Regular-Shaped Solids

For objects with regular geometric shapes (cube, cuboid, cylinder, sphere):

Procedure:

1. Measure the dimensions (length, width, height, radius, etc.)
2. Calculate the volume using the appropriate formula
3. Measure the mass using a balance
4. Calculate density using: ρ = m ÷ V

Example: To find the density of a cube:

• Measure one side length
• Calculate volume = side³
• Weigh the cube
• Density = mass ÷ volume

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Method 2: Irregular-Shaped Solids (Displacement Method)

For objects with irregular shapes, we use the displacement method to find the volume:

The Displacement Method

Procedure:

1. Fill a measuring cylinder with a known volume of water (V₁)

   • Record the initial water level

2. Submerge the object completely in the water

   • Ensure no air bubbles are trapped
   • Ensure the object is fully underwater

3. Record the new water level (V₂)

4. Calculate the volume of the object:

   • Volume of object = V₂ - V₁

5. Measure the mass of the object using a balance

6. Calculate density:

   • ρ = m ÷ V

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Worked Example 4: Density Using Displacement Method

An irregular stone is placed in a measuring cylinder containing 50 ml of water. The water level rises to 75 ml. The stone has a mass of 60 g. Calculate the density of the stone in g/cm³.

Solution:

Step 1: Calculate the volume of the stone

• Initial water level (V₁) = 50 ml
• Final water level (V₂) = 75 ml
• Volume of stone = V₂ - V₁ = 75 - 50 = 25 ml
• Since 1 ml = 1 cm³, volume = 25 cm³

Step 2: Identify known values

• Mass (m) = 60 g
• Volume (V) = 25 cm³

Step 3: Calculate density

• ρ = m ÷ V
• ρ = 60 ÷ 25 = 2.4 g/cm³

Answer: The density of the stone is 2.4 g/cm³.

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Method 3: Measuring Density of Liquids

To find the density of a liquid:

Procedure:

1. Measure the mass of an empty measuring cylinder (m₁)

2. Pour a known volume of the liquid into the cylinder

   • Record the volume (V)

3. Measure the combined mass of the cylinder and liquid (m₂)

4. Calculate the mass of the liquid:

   • Mass of liquid = m₂ - m₁

5. Calculate density:

   • ρ = (m₂ - m₁) ÷ V

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Worked Example 5: Density of a Liquid

To find the density of oil, a student:

• Measures the mass of an empty measuring cylinder: 120 g
• Pours 50 cm³ of oil into the cylinder
• Measures the combined mass: 164 g

Calculate the density of the oil in g/cm³.

Solution:

Step 1: Calculate the mass of the oil

• Mass of empty cylinder (m₁) = 120 g
• Combined mass (m₂) = 164 g
• Mass of oil = m₂ - m₁ = 164 - 120 = 44 g

Step 2: Identify known values

• Mass of oil (m) = 44 g
• Volume of oil (V) = 50 cm³

Step 3: Calculate density

• ρ = m ÷ V
• ρ = 44 ÷ 50 = 0.88 g/cm³

Answer: The density of the oil is 0.88 g/cm³.

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Common Densities of Materials

Knowing typical densities helps you identify materials and check if your calculations are reasonable:

Material	Density (g/cm³)	Density (kg/m³)
Air	0.0012	1.2
Styrofoam	0.05	50
Wood (pine)	0.5	500
Water	1.0	1000
Aluminum	2.7	2700
Iron	7.9	7900
Lead	11.3	11300
Gold	19.3	19300

Key reference point: Water has a density of 1.0 g/cm³ or 1000 kg/m³. Objects denser than water sink; objects less dense float.

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Common Student Misconceptions and Errors

Misconception 1: Density Changes with Size

❌ Wrong: “A larger object has higher density”

✅ Correct: Density is an intrinsic property. It doesn’t change with the size of the object. A small piece of lead and a large piece of lead have the same density.

Why students get confused: They see that a larger object weighs more and think the density has changed.

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Misconception 2: Mass and Density Are the Same

❌ Wrong: “A heavy object has high density”

✅ Correct: Mass and density are different. A large piece of wood can have more mass than a small piece of lead, but lead has higher density.

Clarification:

• Mass = total amount of matter
• Density = mass per unit volume

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Misconception 3: Density Can Be Negative

❌ Wrong: “Density can be negative”

✅ Correct: Density is always positive. It represents mass per unit volume, which are both positive quantities.

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Misconception 4: All Liquids Have the Same Density

❌ Wrong: “All liquids have density of 1 g/cm³”

✅ Correct: Different liquids have different densities. Water is 1.0 g/cm³, but oil is typically 0.8-0.9 g/cm³, and mercury is 13.6 g/cm³.

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Common Exam Errors to Avoid

Error 1: Wrong Units in Final Answer

❌ Wrong: “The density is 2.5” (no units)
✅ Correct: “The density is 2.5 g/cm³”

Examiner tip: Always include units in your final answer. Units are worth marks!

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Error 2: Unit Conversion Mistakes

❌ Wrong: Mixing kg/m³ with g/cm³ without converting
✅ Correct: Convert all units to be consistent before calculating

Example: If mass is in kg and volume is in cm³, convert one or the other to match.

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Error 3: Incorrect Volume Calculation

❌ Wrong: Using wrong formula for volume (e.g., using area formula instead of volume)
✅ Correct: Use the correct volume formula for the shape

Common mistake: Using length × width (area) instead of length × width × height (volume) for a cuboid.

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Error 4: Displacement Method Errors

❌ Wrong: Not fully submerging the object or having air bubbles
✅ Correct: Ensure the object is completely underwater with no trapped air

Common mistake: Not reading the meniscus correctly or not accounting for the object’s volume properly.

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Error 5: Forgetting to Subtract Empty Cylinder Mass

❌ Wrong: Using the combined mass (cylinder + liquid) for density calculation
✅ Correct: Subtract the mass of the empty cylinder to get just the liquid mass

Example: If cylinder + liquid = 200 g and empty cylinder = 150 g, the liquid mass is 50 g, not 200 g.

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IGCSE Physics Practice Questions: Density

Test your understanding with these exam-style questions:

Question 1: Basic Density Calculation

A metal cube has sides of length 4 cm and a mass of 320 g. Calculate its density in g/cm³.

Solution:

Step 1: Calculate volume

• Volume = side³ = 4³ = 4 × 4 × 4 = 64 cm³

Step 2: Calculate density

• ρ = m ÷ V
• ρ = 320 ÷ 64 = 5.0 g/cm³

Answer: The density of the metal cube is 5.0 g/cm³.

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Question 2: Density with Unit Conversion

A block of wood has a mass of 2.5 kg and dimensions 20 cm × 15 cm × 10 cm. Calculate its density in kg/m³.

Solution:

Step 1: Convert dimensions to metres

• Length = 20 cm = 20 ÷ 100 = 0.20 m
• Width = 15 cm = 15 ÷ 100 = 0.15 m
• Height = 10 cm = 10 ÷ 100 = 0.10 m

Step 2: Calculate volume in m³

• Volume = length × width × height
• Volume = 0.20 × 0.15 × 0.10 = 0.003 m³

Step 3: Calculate density

• ρ = m ÷ V
• ρ = 2.5 ÷ 0.003 = 833 kg/m³ (to 3 significant figures)

Answer: The density of the wood is 833 kg/m³.

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Question 3: Displacement Method

A student measures the density of an irregular stone:

• Mass of stone: 85 g
• Initial water level: 40 ml
• Final water level: 57 ml

Calculate the density of the stone in g/cm³.

Solution:

Step 1: Calculate volume

• Volume = Final level - Initial level = 57 - 40 = 17 ml
• Since 1 ml = 1 cm³, volume = 17 cm³

Step 2: Calculate density

• ρ = m ÷ V
• ρ = 85 ÷ 17 = 5.0 g/cm³

Answer: The density of the stone is 5.0 g/cm³.

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Question 4: Density of a Liquid

To find the density of a liquid, a student:

• Weighs an empty measuring cylinder: 95 g
• Adds 30 cm³ of the liquid
• Weighs the cylinder with liquid: 122 g

Calculate the density of the liquid in g/cm³.

Solution:

Step 1: Calculate mass of liquid

• Mass of liquid = 122 - 95 = 27 g

Step 2: Calculate density

• ρ = m ÷ V
• ρ = 27 ÷ 30 = 0.90 g/cm³

Answer: The density of the liquid is 0.90 g/cm³.

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Question 5: Finding Volume from Density

A piece of aluminum has a mass of 135 g. The density of aluminum is 2.7 g/cm³. Calculate the volume of the aluminum.

Solution:

Step 1: Rearrange the formula

• ρ = m ÷ V
• V = m ÷ ρ

Step 2: Calculate volume

• V = 135 ÷ 2.7 = 50 cm³

Answer: The volume of the aluminum is 50 cm³.

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Key Formulas Summary

Density Formula

• Density: ρ = m ÷ V
• Where: ρ = density, m = mass, V = volume

Rearranged Formulas

• Mass: m = ρ × V
• Volume: V = m ÷ ρ

Volume Formulas

• Cube: V = s³
• Cuboid: V = l × w × h
• Cylinder: V = π × r² × h
• Sphere: V = (4/3) × π × r³

Unit Conversions

• g/cm³ to kg/m³: Multiply by 1000
• kg/m³ to g/cm³: Divide by 1000
• 1 ml = 1 cm³

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Examiner Tips for Density Questions

1. Always include units: Density answers must have units (g/cm³ or kg/m³)

2. Check unit consistency: Make sure mass and volume units match before calculating

3. Use correct volume formula: Choose the right formula for the shape you’re working with

4. Show your working: Even if you make a calculation error, method marks are awarded for correct formulas

5. Round appropriately: Round your final answer to the number of significant figures requested

6. Check your answer is reasonable: Compare with known densities (e.g., water = 1 g/cm³) to spot errors

7. Displacement method: Ensure the object is fully submerged and no air bubbles are trapped

8. Liquid density: Remember to subtract the mass of the empty container

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Frequently Asked Questions About IGCSE Physics Density

What is density?

Density is the mass per unit volume of a substance. It tells us how much matter is packed into a given space. The formula is: Density = Mass ÷ Volume, or ρ = m ÷ V.

What are the units of density?

Density is measured in:

• kg/m³ (kilograms per cubic metre)
• g/cm³ (grams per cubic centimetre)

To convert: 1 g/cm³ = 1000 kg/m³

How do I calculate density?

Use the formula: ρ = m ÷ V

• Measure the mass (m) using a balance
• Measure or calculate the volume (V)
• Divide mass by volume to get density

How do I find the volume of an irregular object?

Use the displacement method:

1. Fill a measuring cylinder with water (record volume V₁)
2. Submerge the object completely (record new volume V₂)
3. Volume of object = V₂ - V₁

How do I measure the density of a liquid?

1. Measure mass of empty measuring cylinder
2. Pour known volume of liquid into cylinder
3. Measure combined mass of cylinder + liquid
4. Mass of liquid = combined mass - empty cylinder mass
5. Density = mass of liquid ÷ volume

What is the density of water?

Water has a density of 1.0 g/cm³ or 1000 kg/m³. This is an important reference point - objects denser than water sink, objects less dense float.

Does density change with size?

No! Density is an intrinsic property that doesn’t change with the size of the object. A small piece and a large piece of the same material have the same density.

How do I convert between g/cm³ and kg/m³?

• g/cm³ to kg/m³: Multiply by 1000
• kg/m³ to g/cm³: Divide by 1000

Example: 2.7 g/cm³ = 2.7 × 1000 = 2700 kg/m³

How do I avoid common mistakes in density calculations?

1. Always include units in your answer
2. Check unit consistency (make sure mass and volume units match)
3. Use the correct volume formula for the shape
4. For liquids, remember to subtract the empty container mass
5. For displacement method, ensure object is fully submerged
6. Check your answer is reasonable (compare with known densities)

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Related IGCSE Physics Resources

Strengthen your IGCSE Physics preparation with these comprehensive guides:

• IGCSE Physics Mass and Weight - Understanding mass before studying density
• IGCSE Physics Motion - Speed, velocity, acceleration, and motion graphs
• IGCSE Physics Physical Quantities and Measurement Techniques - Foundation concepts including volume measurement
• IGCSE Physics Motion, Forces and Energy - Complete topic coverage with videos, slides, and quizzes
• IGCSE Physics Revision Notes and Syllabus - Complete syllabus overview and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE Physics past papers and exam resources

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