# 3.1.1 Density

### Density

• Density is defined as:

The mass per unit volume of a material

• Objects made from low density materials typically have a low mass
• Similarly sized objects made from high density materials have a high mass
• For example, a bag full of feathers is far lighter compared to a similar bag full of metal
• Or another example, a balloon is less dense than a small bar of lead despite occupying a larger volume
• Density is related to mass and volume by the following equation:

• Gases, for examples, are less dense than solids because the molecules are more spread out (same mass, over a larger volume)

Gases are less dense than solids

• This equation can be rearranged with the help of the formula triangle:

Density, mass, volume formula triangle

• The units of density depend on what units are used for mass and volume:
• If the mass is measured in g and volume in cm3, then the density will be in g/cm3
• If the mass is measured in kg and volume in m3, then the density will be in kg/m3
• This table gives some examples of densities on common materials
• If a material is more dense than water (1000 kg/m3), then it will sink

Approximate Densities of Materials Table

• The volume of an object may not always be given directly, but can be calculated with the appropriate equation depending on the object’s shape

Volumes of common 3D shapes

#### Worked Example

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.

Step 1: List the known quantities

• Mass of slab, m = 73 kg
• Volume of slab, V = 0.04 m × 0.5 m × 0.85 m = 0.017 m3

Step 2: Write out the equation for density

Step 3: Substitute in values

ρ = 73 ÷ 0.017 = 4294 kg/m3

Step 4: Round the answer to two significant figures

ρ = 4300 kg/m3

#### Exam Tip

Make sure you are comfortable converting between units such as metres (m) and centimetres (cm) or grams (g) and kilograms (kg).

• When converting a larger unit to a smaller one, you multiply (×)
• E.g. 125 m = 125 × 100 = 12 500 cm
• When you convert a smaller unit to a larger one, you divide (÷)
• E.g. 5 g = 5 ÷ 1000 = 0.005 or 5 × 10-3 kg

### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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