Volume and Cubic Units

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.

Concept Map 

What have we learned

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