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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.
start text, V, o, l, u, m, e, space, o, f, space, r, e, c, t, a, n, g, u, l, a, r, space, p, r, i, s, m, end text, equals start text, l, e, n, g, t, h, end text, times, start text, w, i, d, t, h, end text, times, start text, h, e, i, g, h, t, end text
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.
start text, V, o, l, u, m, e, end text, equals, start text, l, e, n, g, t, h, end text, times, start text, w, i, d, t, h, end text, times, start text, h, e, i, g, h, t, end text
empty space, equals, 3, times, 2, times, 3
empty space, equals, 18, start text, space, c, u, b, i, c, space, u, n, i, t, s, end text

Example 2:

A rectangular prism with a length of 6 centimeters, a width of 5 centimeters, and a height of 7 centimeters.
start text, V, o, l, u, m, e, end text, equals, start text, l, e, n, g, t, h, end text, times, start text, w, i, d, t, h, end text, times, start text, h, e, i, g, h, t, end text
empty space, equals, 6, times, 5, times, 7
empty space, equals, 210, start text, space, c, u, b, i, c, space, u, n, i, t, s, end text

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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
start text, c, m, end text, cubed
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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
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, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
start text, c, u, b, i, c, space, c, m, end text

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

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