Density (Edexcel GCSE Maths): Revision Notes
Density
What is density?
Density is a measure that tells us how much mass is packed into a given volume of material. Think of it as how tightly the particles of a substance are squeezed together.
The definition of density is: the mass of a material per unit volume.
Different materials have different densities - for example, lead is much denser than wood because the same volume of lead contains much more mass. This fundamental concept helps us understand why some objects float while others sink, and why materials feel heavier or lighter despite having similar sizes.
The density formula triangle
Understanding the relationship between mass, density, and volume is crucial for solving density problems. The formula triangle is a powerful tool that makes calculations straightforward.
The relationship between mass, density, and volume can be shown using a formula triangle:
M
---
D | V
From this triangle, we can work out three different formulas:
- Density = Mass ÷ Volume or
- Volume = Mass ÷ Density or
- Mass = Density × Volume or
To use the triangle, cover up the quantity you want to find, and the remaining letters show you the calculation needed.
Units of density
When working with density calculations, paying attention to units is essential for getting the correct answer.
The most common units for density are:
- g/cm³ (grammes per cubic centimetre)
- kg/m³ (kilogrammes per cubic metre)
Make sure you check which units are being used in exam questions, as this affects your final answer.
Working with density calculations
Finding mass from density and volume
When you know the density and volume of an object, you can calculate its mass using the formula: Mass = Density × Volume
Worked Example: Finding Mass
If an iron bar has a volume of 1.2 m³ and iron has a density of 7870 kg/m³, then:
Step 1: Identify the formula
Step 2: Substitute the values
Step 3: Calculate the result
Finding density from mass and volume
When you know the mass and volume, you can work out the density using: Density = Mass ÷ Volume
This is particularly useful when dealing with prisms, where the volume can be calculated using:
Mixed materials
Sometimes you need to find the density of a mixture. This requires careful calculation of total mass and total volume.
Steps for calculating density of mixed materials:
- Work out the masses of each material
- Add the masses together to get total mass
- Add the volumes together to get total volume
- Calculate density using: Density = Total mass ÷ Total volume
Exam tips
Exam Strategy Tips:
- Always write down the formula triangle at the start of density questions
- Check your units carefully - make sure mass and volume units match the required density units
- When working with prisms, remember to calculate the volume first using cross-sectional area × length
- Show all your working clearly, even for simple calculations
Remember!
Key Points to Remember:
- Density measures how much mass fits in a given volume
- Use the formula triangle to find the right equation: cover what you're looking for
- Common units are g/cm³ and kg/m³ - check which ones you need
- For prisms: Volume = Cross-sectional area × Length
- Always show your working and check your units in exam questions