KS3

Density

Part ofMathsMeasurement

Key points

An image of three cylindrical measuring beakers. Each beaker is a different size; small, medium, and large. The small beaker contains a blue liquid. The medium beaker contains a red liquid. The large beaker contains a green liquid. — Image caption,
The more dense a substance is, the heavier it feels.

The of an object or substance is its divided by its :

Density = Mass ÷ Volume

The units of density depend on the units used for mass and volume, but are usually g/cm³ (if mass is measured in g and volume in cm³).
The more a substance is, the heavier it feels.
Using the formula Density = Mass ÷ Volume makes it possible to compare the density of objects with different of volume and mass.

An image of three cylindrical measuring beakers. Each beaker is a different size; small, medium, and large. The small beaker contains a blue liquid. The medium beaker contains a red liquid. The large beaker contains a green liquid. — Image caption,
The more dense a substance is, the heavier it feels.

How to compare solids and liquids

Substances can be compared using density:
- If two liquids that are mixed have a different density then the least dense liquid would float to the top.
- Different types of wood have a different density. A hardwood has a greater density and would feel heavier than a softwood.
- Objects that are more dense take up less space than the same mass of a less dense material. For example, a tonne of feathers would take up a far greater volume of space compared to a metric tonne of bricks.

Examples

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When different liquids are mixed together in the same container, their densities will affect what then happens. It will depend on the density of the each of the liquids. If the liquids are different colours it is easier to see the physical effect of density.
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A small amount of five different liquids are added to one container: vegetable oil, water, washing up liquid, maple syrup and honey.
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The liquid which is the most dense (honey) sinks to the bottom of the container. The liquid which is the least dense (vegetable oil) floats to the top of the container. The different colours of the liquids make it easier to see the effect of density.
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Solids have different densities too. Two metal bars, one made from aluminium and the other from copper, are the same size and therefore have the same volume. If the two bars were picked up, one would feel heavier, because it has a greater density.
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The density of aluminium is 2.70g/cm³. The density of copper is 8.95g/cm³. Copper has the greater density. If the two bars are the same size then the one made from copper would feel heavier.
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Density = Mass ÷ Volume. There are many units of mass and volume covering many different magnitudes. As a result there is a large number of units that describe density, a common one being g/cm³. If the densities of two different substances are given in the same units then it is possible to compare their relative densities.

Question

Record these three precious metals in terms of their , from greatest density to lowest density.

A table with two columns; metal, and density measured in grams per centimetres cubed. The first row is populated with copper and eight point six four grams per centimetres cubed. The second row is populated with gold and nineteen point three grams per centimetres cubed. The third row is populated with silver and ten point five grams per centimetres cubed. The labels for the column titles are highlighted purple.

How to work out density

Density is the mass per unit . It can be measured in several ways:
- A common way to calculate the density of any solid, liquid or gas is to divide its in grams (g) by its volume in cubic centimetres (cm³).
- If the object is large, then the density would be calculated by dividing the mass in kilograms (kg) by its volume in cubic metres: Density = Mass ÷ Volume.
- The units for density will result from the units provided for the mass and the volume.

Example

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Calculate the density of these different types of metals.
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The volume and mass of each object is needed to compare the density of the two different metals. The lead pipe has a mass of 2268 grams and a volume of 200 cm³. The iron bar has a mass of 3537 grams and volume of 450 cm³.
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The formula of Density = Mass ÷ Volume must be used to calculate the density of each type of metal.
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The Mass, Density, Volume triangle can be used to help remember the formula.
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The density of the lead pipe is 2268 grams ÷ 200 cm³ = 11.34 g/cm³.
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The density of the iron bar is 3537 grams ÷ 450 cm3 = 7.86 g/cm³.
Image caption,
Lead has a greater density than iron. The density of the lead is 11.34 g/cm³. The density of the iron is 7.86 g/cm³. If a block of lead and a block of iron were the same size then the lead would have a larger mass than the iron, which means that the lead would be heavier.

Question

What is the density of a gold necklace that has a mass of 57 grams and a volume of 3 cm³?

An image of a gold necklace. Written below: mass equals fifty seven grams. Written beneath: volume equals three centimetres cubed.

Practise your understanding of density

Quiz

Practise your knowledge of using density in maths with this quiz. You may need a pen and paper to help you with your answers.

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