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10.05 Volume and capacity


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


Example 1

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

An open box
\text{ mm}^3
\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.

Worked Solution
Create a strategy

Use the table of examples below to help you.

\text{Glass of water}300\text{ mL}
\text{Carton of milk}2\text{ L}
\text{Water usage per person per day}200\text{ L}
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).

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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}



Connect volume and capacity and their units of measurement

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