Compound measures combine two different units to describe how one quantity relates to another. In this topic, the focus is on density, population density and flow rates, which are used to describe physical and real life situations.

 

 

Density

Density describes how much mass is packed into a given volume.

 

Density is calculated using:
$$
density = \frac{mass}{volume}
$$

 

Common units for density include:
• \( kg/m^3 \) kilograms per cubic metre
• \( g/cm^3 \) grams per cubic centimetre

 

 

Interpreting Density

A high density means a large mass is contained in a small volume.

 

A low density means a small mass is spread over a large volume.

 

For example, a substance with a density of \( 8\ g/cm^3 \) is denser than one with a density of \( 2\ g/cm^3 \).

 

When using density:
• mass must be in compatible units
• volume must be in compatible units

 

Always convert units before substituting into the formula.

 

 

Population Density

Population density measures how many people live in a given area.

 

Population density is calculated using:
$$
population\ density = \frac{population}{area}
$$

 

A common unit is:
• \( population\ per\ km^2 \)

 

 

Interpreting Population Density

A high population density means many people live in a small area.

 

A low population density means people are spread out over a large area.

 

For example, a city may have a population density of \( 5000\ per\ km^2 \), while a rural area may have a population density of \( 50\ per\ km^2 \).

 

Population density is useful for comparing how crowded different areas are.

 

 

Flow Rates

A flow rate measures how much substance passes a point in a given time.

 

Flow rate is calculated using:
$$
flow\ rate = \frac{volume}{time}
$$

 

Common units for flow rate include:
• \( m^3\ per\ hour \)
• \( litres\ per\ second \)

 

 

Interpreting Flow Rates

A larger flow rate means a greater volume moves each second or hour.

 

For example, a flow rate of \( 3\ litres\ per\ second \) means 3 litres pass a point every second.

 

Flow rates are used in contexts such as:
• water flowing through pipes
• fuel usage
• air movement

 

 

Using Compound Measures Correctly

When using compound measures:

• identify the quantities involved
• ensure all units are compatible
• substitute values into the correct formula
• state the final answer with correct units

 

Units are as important as the numerical answer

 

 

Key Points to Remember

Density is mass divided by volume.
Common density units include \( kg/m^3 \) and \( g/cm^3 \).
Population density is population divided by area.
Population density is often measured per square kilometre.
Flow rate is volume divided by time.
Flow rate units include \( m^3\ per\ hour \) and \( litres\ per\ second \).

 

Understanding and using compound measures allows physical, environmental and real life situations to be described and compared accurately.