102 LearnersLast updated on July 17th, 2025
Volume of Rectangle
The volume of a rectangle (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 brick, a book, or a box. In this topic, let’s learn about the volume of a rectangle.
What is the volume of a rectangle?
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 Rectangle 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 and then 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 Rectangle?
To derive the volume of a rectangular prism, we use the concept of volume as the total space occupied by a 3D object.
Since a rectangular prism has three dimensions, its volume can be derived as follows: The formula for the volume of any rectangular prism is: Volume = Length × Width × Height Here, the Length, Width, and Height are the dimensions of the prism.
The volume of a rectangular prism will be, Volume = Length × Width × Height
How to find the volume of a rectangle?
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 rectangle: Write down the formula Volume = Length × Width × Height The Length, Width, and Height are the measurements needed to calculate the volume.
Once we know the dimensions, substitute those values in the formula volume = Length × Width × Height To find the volume, multiply the length, width, and height. Volume = Length × Width × Height.
Tips and Tricks for Calculating the Volume of Rectangle
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 just 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, Length = 2, Width = 3, and Height = 4 gives Volume = 2 × 3 × 4 = 24. Check for cubic roots: If you are given the volume and need to find one of the dimensions, you can rearrange the formula accordingly.
Common Mistakes and How to Avoid Them in Volume of Rectangle
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 rectangles.
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 the length, width, and height.
For example, the volume is Length × Width × Height, not adding up face areas.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the perimeter of a rectangle instead of the volume formula.
Volume is the space inside the rectangular 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 cubes
Some kids use the formula for the volume of a cube (side³) instead of the rectangular prism formula when all sides are not equal.
Mistake 4
Confusing cubic volume with linear volume
Thinking of volume in terms of linear measurements.
This happens when someone uses the dimensions (which are linear measurements) without multiplying them to understand that volume relates to cubic measurements.
Mistake 5
Incorrectly calculating one of the dimensions
Some students calculate the given volume with solving for one of the dimensions.
For example, if the volume is given, and they need to find one dimension, they might forget to rearrange the formula and solve properly.
Volume of Rectangle Examples
Problem 1
A rectangular box has dimensions of 2cm, 3cm, and 5cm. What is its volume?
The volume of the rectangular box is 30 cm³.
Explanation
To find the volume of a rectangular prism, use the formula: V = Length × Width × Height Here, the dimensions are 2cm, 3cm, and 5cm, so: V = 2 × 3 × 5 = 30 cm³
Problem 2
A book has dimensions of 10cm, 15cm, and 2cm. Find its volume.
The volume of the book is 300 cm³.
Explanation
To find the volume of a rectangular prism, use the formula: V = Length × Width × Height Substitute the dimensions (10cm, 15cm, 2cm): V = 10 × 15 × 2 = 300 cm³
Problem 3
The volume of a rectangular prism is 120 cm³. If the length is 4cm and the width is 5cm, what is the height?
The height of the prism is 6 cm.
Explanation
If you know the volume of the rectangular prism and two dimensions, you’ll rearrange the formula to find the missing dimension. Volume = Length × Width × Height 120 = 4 × 5 × Height Height = 120 / (4 × 5) Height = 6 cm
Problem 4
A brick has dimensions of 8 inches, 4 inches, and 2 inches. Find its volume.
The volume of the brick is 64 inches³.
Explanation
Using the formula for volume: V = Length × Width × Height Substitute the dimensions 8 inches, 4 inches, 2 inches: V = 8 × 4 × 2 = 64 inches³
Problem 5
You have a storage box with dimensions of 6 feet, 3 feet, and 2 feet. How much space (in cubic feet) is available inside the box?
The box has a volume of 36 cubic feet.
Explanation
Using the formula for volume: V = Length × Width × Height
Substitute the dimensions 6 feet, 3 feet, 2 feet: V = 6 × 3 × 2 = 36 ft³
FAQs on Volume of Rectangle
1.Is the volume of a rectangle 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 of the dimensions?
4.Can the dimensions be decimals or fractions?
5.Is the volume of a rectangle the same as the surface area?
Important Glossaries for Volume of Rectangle
- Length: One of the three dimensions of a rectangular prism, usually the longest side.
- Width: Another dimension of a rectangular prism, typically the shorter side when compared to the length.
- Height: The third dimension of a rectangular prism, often considered the vertical side.
- 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).
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
