100 LearnersLast updated on July 17th, 2025
Volume of Cuboid
The volume of a cuboid is the total space it occupies or the number of cubic units it can hold. A cuboid is a 3D shape with six rectangular faces. To find the volume of a cuboid, we multiply its length, width, and height. In real life, kids relate to the volume of a cuboid by thinking of things like a shoebox, a refrigerator, or a book. In this topic, let’s learn about the volume of the cuboid.
What is the volume of the cuboid?
The volume of a cuboid is the amount of space it occupies.
It is calculated by using the formula: Volume = Length x Width x Height Where 'Length', 'Width', and 'Height' are the dimensions of the cuboid.
Volume of Cuboid Formula A cuboid is a 3-dimensional shape where the opposite faces are equal in size.
To calculate its volume, you multiply the length, width, and height.
The formula for the volume of a cuboid is given as follows: Volume = Length x Width x Height
How to Derive the Volume of a Cuboid?
To derive the volume of a cuboid, we use the concept of volume as the total space occupied by a 3D object.
The formula for the volume of a cuboid is: Volume = Length x Width x Height In this shape, the sides can be different, so you need to multiply each dimension together to get the volume.
How to find the volume of a cuboid?
The volume of a cuboid 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 cuboid: Write down the formula Volume = Length x Width x Height The 'Length', 'Width', and 'Height' are the measurements of the three different edges of the cuboid.
Once we know these measurements, substitute their values in the formula. To find the volume, multiply the length by the width and then by the height.
Tips and Tricks for Calculating the Volume of a Cuboid
Remember the formula: The formula for the volume of a cuboid is: Volume = Length x Width x Height Break it down:
The volume is how much space fits inside the cuboid. Multiply the three different dimensions.
Simplify the numbers: If the dimensions are simple numbers like 2, 3, or 4, it is easy to calculate.
For example, 2 x 3 x 4 = 24.
Check for division If you are given the volume and need to find one dimension, you can divide the volume by the product of the other two dimensions.
For example, if the volume is 24 and two dimensions are 2 and 3, then the third dimension is 24 / (2 x 3) = 4.
Common Mistakes and How to Avoid Them in Volume of Cuboid
Making mistakes while learning the volume of the cuboid is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of cuboids.
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 the faces, but volume is calculated by multiplying Length x Width x Height.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the cuboid’s perimeter instead of the volume formula. Volume is the space inside the cuboid, 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 Cubes
Some kids use the formula for the volume of a cube (side³) instead of the cuboid formula.
Mistake 4
Confusing cubic volume with linear volume
Thinking of volume in terms of linear measurements.
This happens when someone uses a single dimension instead of understanding that volume relates to cubic measurements.
Mistake 5
Incorrectly calculating one dimension
Some students calculate the given volume while solving for one missing dimension. For example, if the volume is given and they need to find one dimension, they might forget to divide by the product of the other two dimensions.
Volume of Cuboid Examples
Problem 1
A cuboid has a length of 5 cm, a width of 3 cm, and a height of 4 cm. What is its volume?
The volume of the cuboid is 60 cm³.
Explanation
To find the volume of a cuboid, use the formula: V = Length x Width x Height Here, the dimensions are 5 cm, 3 cm, and 4 cm, so: V = 5 x 3 x 4 = 60 cm³
Problem 2
A cuboid has a length of 7 m, a width of 2 m, and a height of 6 m. Find its volume.
The volume of the cuboid is 84 m³.
Explanation
To find the volume of a cuboid, use the formula: V = Length x Width x Height Substitute the dimensions (7 m, 2 m, and 6 m): V = 7 x 2 x 6 = 84 m³
Problem 3
The volume of a cuboid is 150 cm³. If its length is 5 cm and width is 5 cm, what is the height of the cuboid?
The height of the cuboid is 6 cm.
Explanation
If you know the volume of the cuboid and two dimensions, divide the volume by the product of these dimensions to find the third dimension. V = Length x Width x Height 150 = 5 x 5 x Height Height = 150 / (5 x 5) = 6 cm
Problem 4
A cuboid has a length of 3.5 inches, a width of 2 inches, and a height of 4 inches. Find its volume.
The volume of the cuboid is 28 inches³.
Explanation
Using the formula for volume: V = Length x Width x Height Substitute the dimensions (3.5 inches, 2 inches, and 4 inches): V = 3.5 x 2 x 4 = 28 inches³
Problem 5
You have a cuboid-shaped tank with a length of 2 feet, a width of 3.5 feet, and a height of 5 feet. How much space (in cubic feet) is available inside the tank?
The tank has a volume of 35 cubic feet.
Explanation
Using the formula for volume: V = Length x Width x Height Substitute the dimensions (2 feet, 3.5 feet, and 5 feet): V = 2 x 3.5 x 5 = 35 ft³
FAQs on Volume of Cuboid
1.Is the volume of a cuboid 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 cuboid the same as the surface area?
Important Glossaries for Volume of Cuboid
- Length: One of the dimensions of a cuboid, the longest side.
- Width: One of the dimensions of a cuboid, usually the shorter side when viewing the face.
- Height: The vertical dimension of a cuboid when it is oriented on a base.
- Volume: The amount of space enclosed within a 3D object, calculated by multiplying Length x Width x Height. It is expressed in cubic units (e.g., cm³, m³).
- Cubic units: The units of measurement used for volume. If 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
