103 LearnersLast updated on June 24th, 2025
Volume of Cube
The volume of a cube is the total space it occupies or the number of cubic units it can hold. A cube is a 3D shape with six square faces, all of equal sizes. To find the volume of a cube, we multiply its length, width, and height. In real life, kids relate to the volume of a cube by thinking of things like an ice cube, a dice, or a Rubik’s cube. In this topic, let’s learn about the volume of the cube.
What is the volume of the cube?
The volume of a cube is the amount of space it occupies. It is calculated by using the formula:
Volume = side3
Where ‘side’ is the length of any edge of the cube.
Volume of Cube Formula
A cube is a 3-dimensional shape where all edges are equal in length. To calculate its volume, you multiply the length of one side by itself three times (since a cube has equal length, width, and height).
The formula for the volume of a cube is given as follows:
Volume = side3
Volume of cube = a x a x a
How to Derive the Volume of a Cube?
To derive the volume of a cube, we use the concept of volume as the total space occupied by a 3D object. Since a cube has equal sides, its volume can be derived as follows:
The formula for the volume of any rectangular prism, including cube is:
Volume = Length x Width x Height
For a cube:
Length = Width = height = a (since all sides are equal)
The volume of a cube will be,
Volume = a x a x a
Volume = a3
How to find the volume of a cube?
The volume of a cube is always expressed in cubic units, for example, cubic centimeters' cm3, cubic meters m3. Cube the side length, and multiply it by three times, to find the volume. Let’s take a look at the formula for finding the volume of a cube:
- Write down the formula
Volume = side3
The side is the length of one edge of the cube.
- The side length of a cube is the length of one of its edges. This is the only measurement needed to calculate the volume because all the sides of a cube are equal.
- Once we know the length of the side, substitute that value for ‘side’ in the formula volume = side3
- To find the volume, cube the side length, meaning multiply the side length by three times.
Volume = side x side x side.
Tips and Tricks for Calculating the Volume of Cube
Remember the formula:
The formula for the volume of a cube is simple:
Volume = side3
Break it down:
The volume is how much space fits inside the cube. And since all the sides are equal, you just need to multiply the side length three times.
Simplify the numbers:
If the side length is a simple number like 2, 3, or 4, it is easy to cube, For example, 33 = 27 and 43 = 64.
Check for cube roots
If you are given the volume and need to find the side length, you can find the cube root. For example, if the volume is 64, then the side length is 364 = 4.
Common Mistakes and How to Avoid Them in Volume of Cube
Making mistakes while learning the volume of the cube is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of 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 6 x side2, but volume is calculated by cubing the side length. For example, the volume is side3, not 6 x side2.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the cube’s perimeter instead of the volume formula. Volume is the space inside the 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 rectangular prisms
Some kids use the formula for the volume of a rectangular prism (length x width x height) instead of the cube 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 the side length
Some students calculate the given volume with solving for the side length. For example, if the volume is given, and they need to find the side, they might forget to take the cube root of the volume.
Volume of Cube Examples
Problem 1
A cube has a side length of 4cm. What is its volume?
The volume of a cube is 64 cm3.
Explanation
To find the volume of a cube, use the formula :
V= side3
Here, the side length is 4cm, so:
V= 43 = 4 x 4 x 4 = 64 cm3
Problem 2
A cube has a side length of 10 m. Find its volume.
The volume of a cube is 1000 m3.
Explanation
To find the volume of a cube, use the formula :
V= side3
Substitute the side length (10 m):
V = 103 = 10 x 10 x 10
= 1000 m3
Problem 3
The volume of a cube is 125 cm³. What is the side length of the cube?
The side length of the cube is 5 cm.
Explanation
If you know the volume of the cube, and you need to find the side length, you’ll take the cube root of the volume.
The formula for the side length s is :
S = ∛125
= 5 cm
Problem 4
A cube has a side length of 2.5 inches. Find its volume.
The volume of the cube is 15.625 inches³.
Explanation
V = side3
Substitute the side length 2.5 inches:
V = 2.53 = 2.5 x 2.5 x 2.5 = 15.625 inches3
Problem 5
You have a cube-shaped box with a side length of 3 feet. How much space (in cubic feet) is available inside the box?
The box has a volume of 27 cubic feet.
Explanation
Using the formula for volume:
V = side3
Substitute the side length 3 feet :
V = 33 = 3 x 3 x 3 = 27 ft3
FAQs on Volume of Cube
1.Is the volume of a cube the same as the surface area?
2.How do you find the volume if the side length is given?
3.What if I have the volume and need to find the side length?
4.Can the side length be a decimal or fraction?
5.Is the volume of a cube the same as the surface area ?
6.How can children in Oman use numbers in everyday life to understand Volume of Cube ?
7.What are some fun ways kids in Oman can practice Volume of Cube with numbers?
8.What role do numbers and Volume of Cube play in helping children in Oman develop problem-solving skills?
9.How can families in Oman create number-rich environments to improve Volume of Cube skills?
Important Glossaries for Volume of Cube
- Side : The length of one of the cube’s edges. Since all edges of a cube are equal, the side length is the same for each edge.
- Volume : The amount of space enclosed within a 3D object. In the case of a cube, the volume is calculated by cubing the side length. It is expressed in cubic units (e.g., cm3, m3).
- Cubic units : The units of measurement used for volume. If the side length is in centimeters (cm), the volume will be cubic centimeters (cm3), if in meters, it will be in cubic meters (m3).
