Volume is the amount of space that an object takes up. We can measure volume with unit cubes, like the one below.
These are called unit cubes because each one represents cubic unit. The volume of a figure is the number of unit cubes that make it up.
For example, let's find the volume of the figure below:
The figure consists of cubes.
Therefore, its volume is cubic units.
We can use metric and customary units to measure volume.
Consider the cube below, whose length, width, and height all equal centimeter.
Since the length, width, and height of this cube all equal centimeter, the volume of this cube is cubic centimeter.
Commonly used metric units of volume are:
cubic meters
cubic centimeters
cubic millimeters
Commonly used customary units of volume are:
cubic feet
cubic inches
We'll learn more about units of volume in future lessons.
If each cube represents one cubic unit, what is the volume of the figure?
The figure consists of cubes.
Therefore, the volume is cubic units.
If each cube represents $1$ cubic unit, what is the volume of the figure?
|
a
|
$5$ cubic units |
|
b
|
$7$ cubic units |
|
c
|
$6$ cubic units |
|
d
|
$9$ cubic units |
|
e
|
$8$ cubic units |
If each cube represents $1$ cubic centimeter, what is the volume of the figure?
|
a
|
$5$ cubic centimeters |
|
b
|
$9$ cubic centimeters |
|
c
|
$8$ cubic centimeters |
|
d
|
$7$ cubic centimeters |
|
e
|
$6$ cubic centimeters |
If each cube represents cubic unit, what is the volume of the figure?
The figure consists of rows, and each row has cubes.
So, there are cubes in total.
Therefore, the volume of the figure is cubic units.
If each cube represents $1$ cubic unit, what is the volume of the figure?
|
a
|
$19$ cubic units |
|
b
|
$18$ cubic units |
|
c
|
$21$ cubic units |
|
d
|
$22$ cubic units |
|
e
|
$20$ cubic units |
If each cube represents $1$ cubic inch, what is the volume of the figure?
|
a
|
$8$ cubic inches |
|
b
|
$12$ cubic inches |
|
c
|
$10$ cubic inches |
|
d
|
$6$ cubic inches |
|
e
|
$5$ cubic inches |
If a figure has multiple layers, we can find its volume by first finding the volume of each layer and then adding the results.
Each cube in the figure below represents one cubic unit. Let's find its volume.
The figure consists of two layers:
The bottom layer consists of cubes.
The top layer consists of cubes, too.
Therefore, the volume is cubic units.
An object is assembled as shown below. Given that each small cube represents one cubic unit, what is the volume of the object?
The figure consists of two layers:
The bottom layer consists of cubes.
The top layer consists of cube.
Therefore, the volume is cubic units.
An object is assembled as shown above. Given that each small cube represents one cubic unit, what is the volume of the object?
|
a
|
$2$ cubic units |
|
b
|
$3$ cubic units |
|
c
|
$4$ cubic units |
|
d
|
$5$ cubic units |
|
e
|
$6$ cubic units |
An object is assembled as shown above. Given that each small cube represents one cubic foot, what is the volume of the object?
|
a
|
$8$ cubic feet |
|
b
|
$9$ cubic feet |
|
c
|
$10$ cubic feet |
|
d
|
$12$ cubic feet |
|
e
|
$11$ cubic feet |