Topics
10. 3D Measurement
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AustraliaNSW
Stage 3

10.03 Volume of rectangular prisms

Lesson
Practice
Lesson

Are you ready?

Let's review how to find the area of a rectangle to help us in this lesson.

Examples

Example 1

Find the area of the rectangle shown.

A rectangle with a length of 12 centimetres and a width of 2 centimetres.
Worked Solution
Create a strategy

Use the area of a rectangle formula: \text{Area}=\text{Length} \times \text{Width}

Apply the idea

We can see that length is 12 \text{ cm} and the width is 2 \text{ cm}.

\displaystyle \text{Area}\displaystyle =\displaystyle \text{Length} \times \text{Width}Use the formula
\displaystyle =\displaystyle 12 \times 2 Substitute the length and width
\displaystyle =\displaystyle 24 \text{ cm}^2Double 12
Idea summary

When we calculate area, the unit of measurement is squared. If we have sides measured in centimetres \text{(cm)}, for example, the area will be \text{cm}^2.

Volume with unit cubes

Let's look at how we can use unit cubes to find the volume of an object.

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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.

Volume of rectangular prisms

Let's see how to calculate the volume of rectangular prisms in this video.

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Examples

Example 3

Find the volume of the rectangular prism shown.

A rectangular prism of length 4 centimeters, width 2 centimeters and a height of 3 centimeters.
Worked Solution
Create a strategy

We can find the volume of a rectangular prism using the formula:

\text{Volume of a rectangular prism}=\text{Length}\times\text{Width}\times\text{Height}

Apply the idea
\displaystyle \text{Volume}\displaystyle =\displaystyle 4\times2\times3Substitute length, width and height
\displaystyle =\displaystyle 8\times3Find 4\times2
\displaystyle =\displaystyle 24\text{ cm}^3Find 8\times3
Idea summary

When we find the volume of a rectangular prism, we need to multiply together three measurements:

  • length (l)

  • width (w)

  • breadth (b)

Sometimes we refer to these measurements as length, width and height.

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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