Learning Objectives
- understand density as mass per unit volume;
- use density = mass ÷ volume;
- rearrange the density formula;
- convert units correctly;
- solve practical problems involving mass, volume and density.
Introduction
This lesson develops Density from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Visual Exploration
Use the diagrams, tables or examples in this lesson to identify what changes, what stays fixed and which relationship connects the values.
What Is Density?
Density tells us how much mass is packed into each unit of volume.
Visual Idea
Worked Example
A metal block has mass 540 g and volume 60 cm³. Find its density.
ρ = m ÷ V.
ρ = 540 ÷ 60 = 9 g/cm³.
Unit Awareness
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Practice Questions
Foundation- Find density if mass is 360 g and volume is 120 cm³.
- Find mass if density is 7.8 g/cm³ and volume is 25 cm³.
- Find volume if mass is 480 kg and density is 2400 kg/m³.
- A cuboid 10 cm by 5 cm by 4 cm has mass 1.6 kg. Find density in g/cm³.
- A liquid has density 0.8 g/cm³. Find mass of 2.5 litres.
- A solid cylinder has radius 3 cm, height 10 cm and mass 848.2 g. Find its density using π≈3.142.
✅ Check Your Work
Show practice answers
- 3 g/cm³.
- 195 g.
- 0.2 m³.
- Volume=200 cm³; mass=1600 g; density=8 g/cm³.
- 2.5 L=2500 cm³; mass=0.8×2500=2000 g=2 kg.
- Volume=πr²h=3.142×9×10=282.78 cm³; density≈3 g/cm³.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Density is mass per unit volume.
- ρ=m/V.
- Keep units consistent.
- Higher density means more mass packed into the same volume.