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Volume of rectangular prisms review

Review the basics of volume and try some practice problems.

What is volume?

Volume is the amount of 3-dimensional space an object occupies. Volume is measured in cubic units.
For example, the rectangular prism below has a volume of 18 cubic units because it is made up of 18 unit cubes.
A rectangular prism made up of unit cubes. The front face shows 9 cubes: 3 rows and 3 columns. The top face of the cube shows 6 cubes: 2 rows and 3 columns. The right-hand side face shows 6 cubes: 3 rows and 2 columns.
Want to learn more about the concept of volume? Check out this video.

Finding volume of a rectangular prism

To find the volume of a rectangular prism, we multiply the length of the prism by the width of the prism by the height of the prism.
Volume of rectangular prism= length×width×height
Want to learn more about finding volume of rectangular prisms? Check out this video.

Example 1:

A rectangular prism made up of unit cubes. The front face of the rectangular prism shows 9 cubes: 3 rows and 3 columns. The top face of the cube shows 6 cubes: 2 rows and 3 columns. The right-hand side face shows 6 cubes: 3 rows and 2 columns. The length of the rectangular prism is 3 units. The width of the rectangular prism is 2 units. The height of the rectangular prism is 3 units.
Volume=length×width×height
Volume=3×2×3
Volume=18 cubic units

Example 2:

A rectangular prism with a length of 6 centimeters, a width of 5 centimeters, and a height of 7 centimeters.
Volume=length×width×height
Volume=6×5×7
Volume=210 cubic units

Practice set 1: Finding volume by multiplying

Problem 1A
What is the volume of the rectangular prism?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
cm3
A rectangular prism with a length of 7 centimeters, a width of 4 centimeters, and a height of 2 centimeters.

Want to try more problems like this? Check out this exercise: Volume 1

Practice set 2: Finding volume with unit cubes

Problem 2A
Unit cube:
A cube has a visible front, right hand side, and top faces.
What is the volume of the rectangular prism?
A rectangular prism made up of unit cubes. The front face of the rectangular prism shows 12 cubes: 3 rows and 4 columns. The top face of the cube shows 8 cubes: 2 rows and 4 columns. The right-hand side face shows 6 cubes: 3 rows and 2 columns.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
unit cubes

Want to try more problems like this? Check out these exercises:
Volume with unit cubes 1
Volume formula intuition

Practice set 3: Challenge items

Problem 3A
The figure below is made up of 2 rectangular prisms.
What is the volume of this figure?
A figure made up of two rectangular prisms. The first rectangular prism has a base that measures 6 centimeters length by 7 centimeters width, and has a height of 1 centimeter. The second rectangular prism sits next to the first rectangular prism. It has a base that measures 3 centimeters length by 7 centimeters width and has a height of 4 centimeters.
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0.75
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
cubic cm

Want to try more problems like this? Check out these exercises:
Decompose figures to find volume
Volume word problems

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