11. 3D Measurement

11.01 Volume using unit cubes

11.02 Units of volume

11.03 Volume of rectangular prisms

11.04 Units of capacity

11.05 Convert units of capacity

11.06 Volume and capacity

11.07 Story problems with volume or capacity

11.08 Units of mass

11.09 Choose the right unit for mass

11.10 Convert units of mass

11.11 Problems with mass

Stage 3

11.01 Volume using unit cubes

Lesson

Ideas

Are you ready?
Volume with unit cubes
Volume with arrays

Are you ready?

We have counted squares to find the area of a shape and can use that to help us find the volume in this lesson. Let's try this problem to review.

Examples

Example 1

Find the area of the shape below.

The image shows an L shape made up of 5 squares. Ask your teacher for more information.

Worked Solution

Create a strategy

Count the total number of squares.

Apply the idea

There are 5 squares inside the shape.

\text{ Area }= 5\, \text{units}^2

Idea summary

To find the amount of space a shape takes up, we can use unit squares.

Volume with unit cubes

This video introduces the unit cube and how it can be used to measure volume (space an object takes up).

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Examples

Example 2

In this figure, 1\text{ block}=1\text{ cm}^3. What is the volume of the solid figure?

An array of cubes with 2 rows and 5 columns.

Worked Solution

Create a strategy

Count the total number of blocks.

Apply the idea

There are 10 blocks in the solid.

\text{Volume}=10\text{ cm}^3

Idea summary

Volume means the amount of space a 3D shape takes up.

To find the volume we can count the number of unit squares that fit inside the shape.

Volume with arrays

What if you cannot see all the blocks? Can we still work out the volume?

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Examples

Example 3

In this figure, 1\text{ block}=1\text{ cm}^3. What is the volume of the solid figure?

An image of a rectangular prism made of unit cubes. Ask your teacher for more information.

Worked Solution

Create a strategy

Multiply the columns by the rows of the array then multiply the answer with the number of sets the solid figure has.

Apply the idea

We can see on the figure that the front face is an array of blocks with 4 rows and 3 columns. We have 2 sets of this face.

\displaystyle \text{Volume}	\displaystyle =	\displaystyle 3\times4\times2	Multiply the columns, rows, and sets
	\displaystyle =	\displaystyle 12\times2	Find 3\times4
	\displaystyle =	\displaystyle 24\text{ cm}^3	Find 12\times2

Idea summary

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

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

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

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