109 LearnersLast updated on July 9th, 2025
Volume of Rectangular Cube
The volume of a rectangular cube, commonly known as a rectangular prism, is the total space it occupies or the number of cubic units it can hold. A rectangular cube is a 3D shape with six rectangular faces, and its opposite faces are equal. To find the volume of a rectangular cube, we multiply its length, width, and height. In real life, kids relate to the volume of a rectangular cube by thinking of things like a shoebox, a book, or a brick. In this topic, let’s learn about the volume of the rectangular cube.
What is the volume of the rectangular cube?
The volume of a rectangular cube is the amount of space it occupies. It is calculated by using the formula: Volume = Length × Width × Height Where the length, width, and height are the dimensions of the rectangular cube.
Volume of Rectangular Cube Formula A rectangular cube is a 3-dimensional shape where its opposite sides are equal.
To calculate its volume, you multiply the length by the width and then by the height. The formula for the volume of a rectangular cube is given as follows: Volume = Length × Width × Height
How to Derive the Volume of a Rectangular Cube?
To derive the volume of a rectangular cube, 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, including a rectangular cube, is: Volume = Length × Width × Height
For a rectangular cube, Volume = Length × Width × Height
How to find the volume of a rectangular cube?
The volume of a rectangular cube 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 cube: Write down the formula Volume = Length × Width × Height
The length, width, and height are the dimensions of the rectangular cube.
Once we know these dimensions, substitute those values into the formula: Volume = Length × Width × Height
To find the volume, multiply the length, width, and height.
Tips and Tricks for Calculating the Volume of Rectangular Cube
- Remember the formula: The formula for the volume of a rectangular cube is simple: Volume = Length × Width × Height
- Break it down: The volume is how much space fits inside the rectangular cube. Multiply the length, width, and height.
- Simplify the numbers: If the measurements are simple numbers like 2, 3, or 4, it is easy to multiply. For example, 2 × 3 × 4 = 24.
- Check for approximate values: If you are given the volume and need to find one dimension, you can use algebra to solve for the unknown dimension.
Common Mistakes and How to Avoid Them in Volume of Rectangular Cube
Making mistakes while learning the volume of the rectangular cube is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of rectangular cubes.
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.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the rectangular cube’s perimeter instead of the volume formula. Volume is the space inside the rectangular cube, 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 cube volume formula (side³) instead of the rectangular cube formula (Length × Width × Height).
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 dimension
Some students calculate the given volume with solving for one dimension. For example, if the volume is given, and they need to find a dimension, they might forget to divide the volume by the known dimensions.
Volume of Rectangular Cube Examples
Problem 1
A rectangular prism 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 rectangular prism is 60 cm³.
Explanation
To find the volume of a rectangular cube, use the formula: V = Length × Width × Height
Here, the length is 5 cm, width is 3 cm, and height is 4 cm, so: V = 5 × 3 × 4 = 60 cm³
Problem 2
A shoebox has a length of 12 inches, a width of 6 inches, and a height of 4 inches. Find its volume.
The volume of the shoebox is 288 inches³.
Explanation
To find the volume of a rectangular cube, use the formula: V = Length × Width × Height
Substitute the length (12 inches), width (6 inches), and height (4 inches): V = 12 × 6 × 4 = 288 inches³
Problem 3
The volume of a rectangular prism is 240 cm³. If its length is 10 cm and its width is 4 cm, what is its height?
The height of the rectangular prism is 6 cm.
Explanation
If you know the volume of the rectangular cube and need to find one dimension, divide the volume by the product of the other two dimensions.
The formula for the height h is: h = Volume ÷ (Length × Width) h = 240 ÷ (10 × 4) h = 6 cm
Problem 4
A brick has a length of 8 inches, a width of 4 inches, and a height of 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 length (8 inches), width (4 inches), and height (2 inches): V = 8 × 4 × 2 = 64 inches³
Problem 5
You have a book with a length of 9 inches, a width of 6 inches, and a height of 1 inch. How much space (in cubic inches) does it occupy?
The book occupies a volume of 54 cubic inches.
Explanation
Using the formula for volume: V = Length × Width × Height
Substitute the length (9 inches), width (6 inches), and height (1 inch): V = 9 × 6 × 1 = 54 inches³
FAQs on Volume of Rectangular Cube
1.Is the volume of a rectangular cube 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.Are the volume and surface area of a rectangular cube the same?
Important Glossaries for Volume of Rectangular Cube
- Length: One of the three dimensions of a rectangular cube, typically the longest side.
- Width: One of the three dimensions of a rectangular cube, typically the shorter side parallel to the length.
- Height: One of the three dimensions of a rectangular cube, typically the vertical side.
- Volume: The amount of space enclosed within a 3D object. In the case of a rectangular cube, 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, the volume 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
