# 10.02 Units of volume

Lesson

## Are you ready

Estimating the  length of objects  can help us in this lesson. Let's try a problem to review.

### Examples

#### Example 1

Choose the best estimate for the length of a fingernail.

A
100 millimetres
B
60 millimetres
C
10 millimetres
D
1 millimetre
Worked Solution
Create a strategy

Use a ruler. The gap between each line is 1 millimetre.

Apply the idea

A sultana has almost the same length of a fingernail. We can see below that a sultana is 9 millimetres.

The closest estimate from the options is 10 millimetres, so the answer is option C.

Idea summary

To estimate the length of an object, we can compare it to an object where we have an idea already of its estimated length.

## Units for volume

Let's look at the units for volume of \text{mm}^3, \text{cm}^3, and \text{m}^3.

### Examples

#### Example 2

Which of these is the bigger volume?

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

Since the options have the same number, choose the option with the bigger unit.

Apply the idea

We know that centimetres \text{(cm)} is bigger than millimetres \text{(mm)}, so the answer is option B.

Idea summary

Here are some units of volume from lightest to heaviest: \text{mm}^3, \text{cm}^3, and \text{m}^3.

## Choose units of volume

How do you know which unit to use?

### Examples

#### Example 3

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

A
\text{ cm}^3
B
\text{ mm}^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 A.

Idea summary

A cubic millimetre \left(\text{mm}^3\right) is about as big as a grain of sand.

A cubic centimetre \left(\text{cm}^3\right) is about as big as the end of your thumb.

A cubic metre \left(\text{m}^3\right) is about as big as a washing machine.

## Estimate volume

Let's look at how we can estimate volume.

### Examples

#### Example 4

The bookshelf shown below has a total volume of 20\,000 \text{ cm}^3.

Select the best estimate for the volume of the books.

A
5000 \text{ cm}^3
B
10\,000 \text{ cm}^3
C
20\,000 \text{ cm}^3
Worked Solution
Create a strategy

Find the portion of the bookshelf that contains books.

Apply the idea

We can see 1 out of the 4 portions of the bookshelf contains books.

So the volume of books will be approximately the same as one quarter of the volume of the bookshelf.

A quarter of 20\,000 \text{ cm}^3 is 5000 \text{ cm}^3. So the best estimate for the volume of the books is option A.

Idea summary

To estimate the volume of an object, we can compare it to a volume that we already know.

### Outcomes

#### VCMMG222

Connect decimal representations to the metric system