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:
- Count the number of cubes in one layer. There are ____ cubes in one layer.
- 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?
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