103 LearnersLast updated on September 5, 2025
Volume of Right Rectangular Prism
The volume of a right rectangular prism is the total space it occupies or the number of cubic units it can hold. A right rectangular prism is a 3D shape with six rectangular faces. To find the volume of a right rectangular prism, we multiply its length, width, and height. In real life, kids relate to the volume of a right rectangular prism by thinking of things like a cereal box, a brick, or a book. In this topic, let’s learn about the volume of the right rectangular prism.
What is the volume of the right rectangular prism?
The volume of a right rectangular prism is the amount of space it occupies. It is calculated using the formula:
Volume = Length x Width x Height
Where 'Length', 'Width', and 'Height' are the dimensions of the prism.
Volume of Right Rectangular Prism Formula: A right rectangular prism is a 3-dimensional shape with rectangular faces.
To calculate its volume, you multiply the length by the width by the height.The formula for the volume of a right rectangular prism is given as follows:
Volume = Length x Width x Height
How to Derive the Volume of a Right Rectangular Prism?
To derive the volume of a right rectangular prism, we use the concept of volume as the total space occupied by a 3D object. A right rectangular prism's volume can be derived as follows:
The formula for the volume of any rectangular prism is:
Volume = Length x Width x Height
This formula applies directly to right rectangular prisms, where the faces meet at right angles.
How to find the volume of a right rectangular prism?
The volume of a right 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 right rectangular prism:
Write down the formula Volume = Length x Width x Height
The dimensions are the length, width, and height of the prism.
Once we know the dimensions, substitute these values into the formula Volume = Length x Width x Height.
Tips and Tricks for Calculating the Volume of Right Rectangular Prism
- Remember the formula: The formula for the volume of a right rectangular prism is simple: Volume = Length x Width x Height
- Break it down: The volume is how much space fits inside the prism. You need to multiply the three dimensions.
- Simplify the numbers: If the dimensions are simple numbers like 2, 3, or 4, it is easy to calculate. For example, if Length = 3, Width = 3, Height = 3, then Volume = 3 x 3 x 3 = 27.
- Think of real-life objects: Visualize objects like boxes or books to understand the concept.
Common Mistakes and How to Avoid Them in Volume of Right Rectangular Prism
Making mistakes while learning the volume of a right 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 right 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 summing the areas of all the faces, but volume is calculated by multiplying the length, width, and height. For example, the volume is Length x Width x Height, not the sum of the face areas.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the prism’s perimeter instead of the volume formula. Volume is the space inside the prism, whereas the 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 cubes
Some kids use the formula for the volume of a cube (side³) instead of the rectangular prism formula.
Mistake 4
Confusing cubic volume with linear volume
Thinking of volume in terms of linear measurements. This happens when someone uses the side length (which is a linear measurement) instead of understanding that volume relates to cubic measurements.
Mistake 5
Incorrectly calculating one or more dimensions
Some students make mistakes when calculating the volume by incorrectly measuring or using the dimensions. Ensure you have the correct length, width, and height values.
Volume of Right Rectangular Prism Examples
Problem 1
A box has dimensions of 5 cm by 3 cm by 2 cm. What is its volume?
The volume of the box is 30 cm³.
Explanation
To find the volume of a right rectangular prism, use the formula: V = Length x Width x Height
Here, Length = 5 cm, Width = 3 cm, Height = 2 cm,
so: V = 5 x 3 x 2 = 30 cm³
Problem 2
A fish tank has a length of 15 m, a width of 4 m, and a height of 3 m. Find its volume.
The volume of the fish tank is 180 m³.
Explanation
To find the volume of a right rectangular prism, use the formula: V = Length x Width x Height
Substitute the dimensions (Length = 15 m, Width = 4 m, Height = 3 m):
V = 15 x 4 x 3 = 180 m³
Problem 3
The volume of a storage container is 200 cm³. If its length is 10 cm and its width is 5 cm, what is its height?
The height of the storage container is 4 cm.
Explanation
If you know the volume of the right rectangular prism and two of its dimensions, solve for the third dimension using the formula:
Volume = Length x Width x Height
200 = 10 x 5 x Height
Height = 200 / (10 x 5) = 4 cm
Problem 4
A brick has dimensions of 8 inches by 4 inches by 2 inches. Find its volume.
The volume of the brick is 64 inches³.
Explanation
Using the formula for volume: V = Length x Width x Height
Substitute the dimensions (Length = 8 inches, Width = 4 inches, Height = 2 inches):
V = 8 x 4 x 2 = 64 inches³
Problem 5
You have a book with dimensions of 12 inches by 9 inches by 2 inches. How much space (in cubic inches) does it occupy?
The book occupies a volume of 216 cubic inches.
Explanation
Using the formula for volume: V = Length x Width x Height
Substitute the dimensions (Length = 12 inches, Width = 9 inches, Height = 2 inches):
V = 12 x 9 x 2 = 216 inches³
FAQs on Volume of Right Rectangular Prism
1.Is the volume of a right 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 right rectangular prism the same as the surface area?
Important Glossaries for Volume of Right Rectangular Prism
- Length: One of the dimensions of the prism, typically the longest side.
- Width: Another dimension of the prism, usually perpendicular to the length.
- Height: The vertical dimension of the prism, perpendicular to both length and width.
- Volume: The amount of space enclosed within a 3D object. In the case of a right rectangular prism, volume is calculated by multiplying the dimensions.
- 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).
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
