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# Volume and Cubic Units

Sep 29, 2022

## Key Concepts

• Volume and cubic units
• Cube and rectangular prism
• Model volume

## Introduction

What is a cubic unit?

A cubic unit is the volume of a cube measuring 1 unit on each edge.

Each cube in the below figure is 1 cubic unit.

What is volume?

Volume is the number of cubic units needed to pack a solid figure without gaps or overlaps.

The volume of an object is measured in cubic units.

### Volume and cubic units

Robert made an art project of a rectangular prism using cubes. His prism is 3 cubes long, 4 cubes wide, and 2 cubes high.

Let us identify the total number of cubes he used by looking at the picture.

Solution: 24 cubes

Each cube in the above figure is 1 cubic unit.

24 cubic units.

### Cube and rectangular prism

#### Cube

A cube is a three-dimensional solid object.

It is bounded by six square faces, facets or sides, with three meeting at each vertex.

#### Rectangular prism

A rectangular prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangles such that every two opposite side faces are identical.

Real-life examples of a rectangular prism:

Example 1:

Find the volume of the bottom layer of the given image.

Step 1: Count the number of cubes.

Step 2: There are 10 cubes on the bottom layer.

Step 3: The volume of the bottom layer is 10 cubic units.

Example 2:

Find the volume of bottom the layer.

Step 1: Count the number of cubes.

Step 2: There are 6 cubes on the bottom layer.

Step 3: The volume of the bottom layer is 6 cubic units.

### Model volume

Example 1:

Find the volume of the rectangular prism.

Step 1:  Count the cubes on the bottom layer of the prism.

4 + 4 =8

8 cubes on bottom layer.

Volume of the bottom layer is 8 cubic units.

Step 2: Count the layers.

Step 3: Multiply the volume of the bottom layer by 3.

3 x 8 = 24

The volume of the prism is 24 cubic units.

Example 2

Find the volume of the rectangular prism.

Step 1:  Count the cubes on the bottom layer of the prism.

4 + 4 =8

8 cubes on each layer.

Volume of bottom layer is 8 cubic units.

Step 2: Count the layers.

Step 3: Multiply the volume of the bottom layer by 2.

2 x 8 = 16

The volume of the prism is 16 cubic units.

## Exercise

• Find the volume of the bottom layer.
• How many layers are there in the image below?
• Find the volume of the bottom layer.
• Find the volume of the rectangular prism.
• Find the volume of the rectangular prism.
• Find the volume of the prism.
• Jan filed the box shown below with unit cubes to find its volume. The unit cubes Jan used have sides of length 1 centimeter. What is the volume of the box?
• Answer the following questions:
1. Count the number of cubes in one layer. There are ____ cubes in one layer.
2. Once you know how many cubes are in one layer, what else do you need to know to find the volume?
• Find the volume of the rectangular prism.

### What have we learned

• Understanding the volume and cubic units
• Understanding cube and rectangular prism
• How to find volume of rectangular prism?

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