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10.03 Volume of rectangular prisms


Are you ready?

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


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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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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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.



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

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