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 1 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 2 cubes.

Therefore, its volume is 2 cubic units.

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We can use metric and customary units to measure volume.

Consider the cube below, whose length, width, and height all equal 1 centimeter.

Since the length, width, and height of this cube all equal 1 centimeter, the volume of this cube is \mathbf 1 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.

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If each cube represents one cubic unit, what is the volume of the figure?

EXPLANATION

The figure consists of 10 cubes.

Therefore, the volume is 10 cubic units.

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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 1 cubic unit, what is the volume of the figure?

EXPLANATION

The figure consists of 3 rows, and each row has 5 cubes.

So, there are 5 \times 3 = 15 cubes in total.

Therefore, the volume of the figure is 15 cubic units.

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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 2 cubes.

  • The top layer consists of 2 cubes, too.

Therefore, the volume is 2+2=4 cubic units.

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An object is assembled as shown below. Given that each small cube represents one cubic unit, what is the volume of the object?

EXPLANATION

The figure consists of two layers:

  • The bottom layer consists of 4 cubes.

  • The top layer consists of 1 cube.

Therefore, the volume is 4+1=5 cubic units.

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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
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