At the end of this lesson, student should be able to:

- Recognize the need for cubic metres
- Understand that measurements of and volume are based on standard units.
- Convert between metric unit of volume

Volume is a measure of the amount of space that a three – dimensional shape occupies. Thus length × breadth × height = volume

Let’s take a look at a diagram of a prism and how volume is calculated.

Volume = length × breadth × height

= 4units × 3 units × 2 units

= 24 units^{3}

To understand what volume means, let’s start by filling the bottom of the prism with unit cubes. This means the bottom of the prism will act as a box will hold as many as possible without stacking them on top of each other. This is what it will look like.

The diagram above does not yet represent the total volume. It only represents a partial volume, but we need to count these cubes to arrive at the total volume.

Since the length is 4 units and the breadth is 3 units, the bottom layer of cube measure rows and columns that are 3units by 4units. So, a quick way of counting the blocks would be to multiply 3 × 4 = 12 units^{2}.

We could stack cubes on top each other until the prism is completely filled. It would be filled so that all cubes are touching each other such that no space existed between cubes. It would look like this.

To count all the cubes above, we already know there are 12 cubes on the bottom level and all levels contain the exact number of cubes. Therefore we need only to take the bottom total of **12 × 2** (since there are 2 levels).

Volume = 12 × 2 = 24 total

**Note:** If we review our calculations, we find that the total bottom layer of cubes was found by multiplying the prisms length by its breadth. Then we took the result and multiplied it by the prism’s height. So,

**Volume of prisms = length × breadth × height**

__Example 1__

Give the volume of the figure below in cubic unit

__Solution__

a)One layer of eight

Volume = 8 cubic unit

b) One layer of 5

Volume = 5 cubic unit

c) Top layer = 3

Middle layer = 2

Bottom layer = 3

Volume = 9 cubic unit

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