10.06 Volume and capacity

Lesson

Ideas

We have looked at  units of volume  and  units of capacity  . It is important that we remember the difference.

Examples

Example 1

What is the most appropriate unit for measuring the volume of a box?

A
\text{ mm}^3
B
\text{ cm}^3
Worked Solution
Create a strategy

Think about what type of objects would be measured by these units.

Apply the idea

\text {mm}^3 is useful to measure a drop of liquid, or the volume of a coin and other tiny objects. \text {cm}^3 is useful to measure bigger objects like a ball or a box.

So, the answer is option B.

Example 2

Choose the most appropriate unit of measure for finding the amount of water in a dam.

A
Millilitres
B
Megalitres
C
Litres
Worked Solution
Create a strategy

Apply the idea

Dams can store massive amounts of water, enough to supply entire cities. Cities have thousands of people, that each use 200\text{ L} of water per day. So it would need to store millions of litres.

A megalitre is equal to a million of litres. So this is the most appropriate unit.

The correct answer is option B.

Idea summary

Volume measures the amount of space an object takes up. Some units are: \text{mm}^3, \,\text{cm}^3, \,\text{m}^3.

Capacity measures the amount of liquid an object can hold. Some units are: \text{mL}, \,\text{L}, \,\text{kL}, \,\text{ML}.

Volume and capacity

Let's look at how to convert between millilitres (\text{mL}) and cubic centimetres (\text{cm}^3).

Examples

Example 3

Convert 40 millilitres (\text{mL}) to cubic centimetres (\text{cm}^3).

Worked Solution
Create a strategy

Use the conversion rule 1 \text{ mL} = 1 \text{ cm}^3.

Apply the idea

Since 1 \text{ mL} = 1 \text{ cm}^3 we don't need to change the number, we just change the units:40 \text{ mL} = 40 \text{ cm}^3

Idea summary

Below are the conversions between volume and capacity:

\begin{array}{c} &\text{Volume} & &\text{Capacity} \\ &1 \text{ cm}^3 &= &1 \text{ mL} \\ &1000 \text{ cm}^3 &= &1 \text{ L} \\ &1 \text{ m}^3 &= &1000 \text{ L} \\ &1 \text{ m}^3 &= &1 \text{ kL} \\ \end{array}

Outcomes

MA3-11MG

selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities, and converts between units of capacity