100 LearnersLast updated on July 17th, 2025
Volume of Rectangular Prism
The volume of a rectangular prism is the total space it occupies or the number of cubic units it can hold. A rectangular prism is a 3D shape with six rectangular faces. To find the volume of a rectangular prism, we multiply its length, width, and height. In real life, kids relate to the volume of a rectangular prism by thinking of things like a shoebox, a book, or a cereal box. In this topic, let’s learn about the volume of rectangular prisms.
What is the volume of a rectangular prism?
The volume of a rectangular prism is the amount of space it occupies.
It is calculated by using the formula: Volume = Length × Width × Height Where 'Length,' 'Width,' and 'Height' are the dimensions of the rectangular prism.
Volume of Rectangular Prism Formula A rectangular prism is a 3-dimensional shape where the length, width, and height can be different.
To calculate its volume, you multiply the length by the width by the height.
The formula for the volume of a rectangular prism is given as follows: Volume = Length × Width × Height
How to Derive the Volume of a Rectangular Prism?
To derive the volume of a rectangular prism, we use the concept of volume as the total space occupied by a 3D object.
The volume can be derived as follows: The formula for the volume of any rectangular prism is: Volume = Length × Width × Height Each dimension can be different, so you multiply these three measures to find the volume.
How to find the volume of a rectangular prism?
The volume of a rectangular prism is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³).
Multiply the length, width, and height to find the volume.
Let’s take a look at the formula for finding the volume of a rectangular prism: Write down the formula Volume = Length × Width × Height The length, width, and height are the dimensions of the rectangular prism.
Once we know these values, substitute them into the formula Volume = Length × Width × Height to find the volume.
Tips and Tricks for Calculating the Volume of Rectangular Prism
Remember the formula: The formula for the volume of a rectangular prism is: Volume = Length × Width × Height Break it down: The volume is how much space fits inside the rectangular prism.
You need to multiply the length, width, and height. Simplify the numbers: Use estimation for simple numbers to quickly calculate.
For example, if Length = 4, Width = 3, and Height = 5, the volume is 60. Check for units: Ensure all dimensions are in the same unit before calculating the volume. If not, convert them to the same unit.
Common Mistakes and How to Avoid Them in Volume of Rectangular Prism
Making mistakes while learning the volume of a rectangular prism is common.
Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of rectangular prisms.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area.
Surface area is calculated by adding the areas of all faces, but volume is calculated by multiplying length, width, and height.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the perimeter of the rectangular prism instead of the volume formula.
Volume is the space inside the prism, whereas perimeter refers to the total length around the edges of a 2D shape.
Do not mix them up.
Mistake 3
Using the wrong Formula for rectangular prisms
Some kids use the formula for the volume of a cube (side³) instead of the correct formula for rectangular prisms (Length × Width × Height).
Mistake 4
Confusing cubic volume with linear volume
Thinking of volume in terms of linear measurements.
This happens when someone uses one dimension (which is a linear measurement) instead of understanding that volume relates to cubic measurements.
Mistake 5
Incorrectly calculating the dimensions
Some students calculate the given volume with solving for one dimension.
For example, if the volume is given, and they need to find one dimension, they might forget to divide by the other two dimensions.
Volume of Rectangular Prism Examples
Problem 1
A rectangular prism has dimensions of 4 cm by 3 cm by 5 cm. What is its volume?
The volume of the rectangular prism is 60 cm³.
Explanation
To find the volume of a rectangular prism, use the formula: V = Length × Width × Height Here, the dimensions are 4 cm, 3 cm, and 5 cm, so: V = 4 × 3 × 5 = 60 cm³
Problem 2
A box has dimensions of 10 m by 2 m by 3 m. Find its volume.
The volume of the box is 60 m³.
Explanation
To find the volume of a rectangular prism, use the formula: V = Length × Width × Height Substitute the dimensions (10 m, 2 m, 3 m): V = 10 × 2 × 3 = 60 m³
Problem 3
The volume of a rectangular prism is 120 cm³. If the length is 4 cm, and the width is 5 cm, what is the height of the prism?
The height of the prism is 6 cm.
Explanation
If you know the volume of the rectangular prism, and you need to find the height, divide the volume by the product of the length and width. H = Volume / (Length × Width) H = 120 / (4 × 5) = 6 cm
Problem 4
A rectangular tank has dimensions of 2.5 m by 3.5 m by 1 m. Find its volume.
The volume of the tank is 8.75 m³.
Explanation
Using the formula for volume: V = Length × Width × Height Substitute the dimensions: V = 2.5 × 3.5 × 1 = 8.75 m³
Problem 5
You have a rectangular storage box with dimensions of 3 feet by 2 feet by 1 foot. How much space (in cubic feet) is available inside the box?
The box has a volume of 6 cubic feet.
Explanation
Using the formula for volume: V = Length × Width × Height Substitute the dimensions: V = 3 × 2 × 1 = 6 ft³
FAQs on Volume of Rectangular Prism
1.Is the volume of a rectangular prism the same as the surface area?
2.How do you find the volume if the dimensions are given?
3.What if I have the volume and need to find one dimension?
4.Can the dimensions be decimals or fractions?
5.Is the volume of a rectangular prism the same as the surface area?
Important Glossaries for Volume of Rectangular Prism
- Length: The measurement of the longest side of the rectangular prism.
- Width: The measurement of the side perpendicular to the length.
- Height: The measurement of the side perpendicular to both the length and width.
- Volume: The amount of space enclosed within a 3D object. In the case of a rectangular prism, the volume is calculated by multiplying the length, width, and height. It is expressed in cubic units (e.g., cm³, m³).
- Cubic units: The units of measurement used for volume. If the dimensions are in centimeters (cm), the volume will be in cubic centimeters (cm³); if in meters, it will be in cubic meters (m³).
Explore More measurement
![Important Math Links Icon]()
Previous to Volume of Rectangular Prism
![Important Math Links Icon]()
Next to Volume of Rectangular Prism
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
