# Rectangular prisms

## Introduction

To find out how much concrete is needed to pour the footpath in this photo you need to know how to calculate the volume of a rectangular prisim.

Do you know how to calculate the volume of rectangular prisms?

## Calculating volume

The formula for calculating **volume** is:

**V**olume = **A**rea by **h**eight

**V **=** A **X** h**

The formula for calculating **area of a rectangle** is:

**A**rea = **l**ength by **w**idth

**A** = **l** X **w**

So the **volume** of a **rectangular prism **can be calculated using the formula:

**V**olume = **l**ength by **w**idth by **h**eight

**V **=** l **X** w **X** h**

For the rectangular prism in the diagram:

**V** = 2 m X 1 m X 1 m

**V** = **2 m³** (cubic metres)

## Exercise 1

Calculate the volume of this rectangular prism.

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## Exercise 2

Calculate the volume of this rectangular prism.

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## Exercise 3

Calculate the volume of this rectangular prism.

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## Exercise 4

Calculate the volume of this rectangular prism.

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## Exercise 5

Calculate the volume of this rectangular prism (measurements in millimetres).

**Before doing calculations convert millimetres to metres.**

Length = 3.5 m

Width = 2.4 m

Height = 2.7 m

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## Exercise 6

Calculate the volume of this rectangular prism (measurements in millimetres).

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## Shapes made of combined rectangular/square prisms

To calculate the volume of this shape you can break it into two rectangular prisms (**RP _{1}** and

**RP**).

_{2}Select this link to see RP_{1} and RP_{2}.

**Method to use:**

**V**olume **t**otal = Volume **RP _{1}** plus Volume

**RP**

_{2}Vt = V

**RP**+ V

_{1}**RP**

_{2}Vt = (l X w X h) + (l X w X h)

Vt = (2 X 1 X 1) + (1 X 1 X 1)

Vt = 3 + 1

**Vt = 3 m³**.

## Exercise 7

Calculate the volume of this object.

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## Exercise 8

Calculate the volume of this object.

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## Exercise 9

Calculate the volume of this object.

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## Summary

This is the end of the section on Rectangular prisms.

Key points to remember are:

- the formula for volume is:

Volume = Area by height - volume of a rectangular prism is calculated using the formula:

Volume = length by width by height - break combined rectangular/square prisms into individual prisms
- calculate the volume of each prism, then add the volumes together.

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