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 1818 cubic units because it is made up of 1818 unit cubes.
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=\text{Volume of rectangular prism}= length×width×height\text{length}\times\text{width}\times\text{height}
Want to learn more about finding volume of rectangular prisms? Check out this video.

Example 1:

Volume=length×width×height\text{Volume}=\text{length}\times\text{width}\times\text{height}
Volume=3×2×3\phantom{\text{Volume}}=3\times2\times3
Volume=18 cubic units\phantom{\text{Volume}}=18\text{ cubic units}

Example 2:

Volume=length×width×height\text{Volume}=\text{length}\times\text{width}\times\text{height}
Volume=6×5×7\phantom{\text{Volume}}=6\times5\times7
Volume=210 cubic units\phantom{\text{Volume}}=210\text{ 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 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
cm3\text{cm}^3

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:
What is the volume of the rectangular prism?
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{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 22 rectangular prisms.
What is the volume of this figure?
  • Your answer should be
  • an integer, like 66
  • an exact decimal, like 0.750.75
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
cubic cm\text{cubic cm}

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