Topics
10. 3D Measurement
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AustraliaNSW
Stage 3

10.02 Units of volume

Lesson
Practice
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.

A ruler showing the gap between 0 and small line next to it measures 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.

A ruler showing a sultana measures 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.

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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?

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Examples

Example 3

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

An open 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.

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Examples

Example 4

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

This image shows a bookshelf with 4 shelves. There are books on the top shelf.

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.

\displaystyle \dfrac{1}{4} \text{ of }20\,000 \displaystyle =\displaystyle \dfrac{1}{2} \text{ of }\dfrac{1}{2} \text{ of }20\,000 Use the half-half strategy
\displaystyle =\displaystyle \dfrac{1}{2} \text{ of }10\,000 Halve 20\,000
\displaystyle =\displaystyle 5\,000 Halve 10\,000

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

MA3-11MG

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

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