Unit Cube is a 3-D object with 12 edges and the length of each edge is one unit. We all know about Dice, Rubik’s Cubes, etc all these are cubes and if their edge length is one then they are called unit cubes.

In this article, we will learn about, the unit cube, the volume of the unit cube, the surface area of the unit cube, and others in detail.

What is a Unit Cube?

A unit cube is a cube with a side length of 1 unit.

A unit cube is a three-dimensional object like the other cubes. Unit Cube contains 12 edges. The length of each edge of a Unit Cube is 1 unit. Unit cube has six faces that are unit squares types.

Now in the above cube if the edge length is 1 unit then the cube is called a unit cube.

Unit Cube Definition

A cube is defined as a Unit Cube when each side equals t 1 unit. Unit Cube is also well known as “Cube of Side 1.”

Volume of Unit Cube

Volume is defined as the amount of space that is occupied by an object. To calculate the volume of a unit cube, we are using the formula of volume of a cube,

Volume = side × side × side = (side)³

Each side of a cube is equal. The length of each side of a unit cube is 1 unit long.

So, Volume of a Unit Cube = (side)³

Volume = (1)³ unit³

Volume = 1 unit³

Thus, volume of a Unit Cube is 1 unit³. This shown in the image added below:

Volume of Unit Cube

How to Find Volume of a Unit Cube?

A unit cube is a type of Cube and each of the edges length is 1 unit long. So, to find the Volume of a Unit Cube , we need only the length of sides. Here, In Unit Cube the length of each side is 1 unit.

Volume of a Unit Cube = side³ = 1³ = 1 unit³

Volume of Unit Cube Formula

To find the Volume of any types of cube, we use the following formula,

Volume of a Cube = (side)³

The side length of a Unit Cube is 1 unit

So, Volume of a Unit Cube = (1)³ unit³

Volume of a Unit Cube = 1 unit³

Volume of Unit Cube Using Diagonal Formula

Another way to find the Volume of Unit Cube is by using Diagonal Formula. We know, the formula of Diagonal of a Cube

Diagonal (d) = √3 × side (s)

Side = Diagonal/√3

Now, We use the volume formula of a cube,

Volume = (side)³

Volume = (Diagonal/√3 )³

Volume = (√3 × Diagonal³)/9

Example: Find the volume of a cube whose diagonal is 3 cm.

Volume = (√3 × Diagonal³)/9

Volume = (√3 × 3³)/9 = 3√3 cm³

Surface Area of Unit Cube

Total area that is covered by all the faces of a three dimensional object, is called the Surface Area. Surface Area is calculated in square units or unit². Formula or surface area of cube is:

Surface Area of Cube = 6 × side²

A Unit Cube has 6 square faces and each face length is 1 unit.

Each face area of a Unit Cube = 1 × 1 unit² = 1 unit²

Now,

Surface Area of a Unit Cube(A) = 6 × Area of Each Face

A = 6 × 1 unit²

A = 6 unit²

Thus, surface area of a Unit Cube is 6 unit².

Why Is Volume Calculated in Cubic Units?

Volume is calculated in cubic units because the formula of volume of a cube is the 3 times multiplication of similar units.

• Volume of a Cube = side × side × side
• Volume of a Cube = unit × unit × unit
• Volume of a Cube = cubic unit (unit³)

Let, the unit be meter,

• Volume = meter × meter × meter
• Volume = meter³ or cubic meter

Volume involves three dimensions: length, width, and height. When we measure each dimension in the same unit (like meters, feet, or centimeters), we multiply them together to find the total volume. This multiplication gives us cubic units because it’s like stacking unit cubes to fill the space.

This is why, volume is calculated in cubic unit or unit³.

Are Unit Cubes and Volume the Same?

No, unit cubes and volume are not same. Unit Cubes are the cubes whose each edge length is 1 unit and the volume of a unit cube is 1 unit³, Whereas Volume is the measurement by the cubic unit.

What Is the Purpose of Unit Cube?

A Unit Cube is a type of Cube whose each edges length is 1 unit long. To find the volume of a solid object, we generally use cubic units. Let us take a solid shape which is made of n unit cubes, each cube has a volume of 1 unit³.

Volume of Solid Shape is is measure in unit cube.

It means that the ‘n’ number of unit cubes can be fit in the solid shape whose total volume is n unit³.

Fun Facts on Unit Cube

Some fun facts on unit cube are:

1. Unit Cube is used for the measurement of volume of any solid shapes.
2. To find the volume of any solid shapes, fill it with the unit cubes. you will get the volume very easily.
3. Volume of any solid shape is equal to the number of unit cubes.

Read More:

• Faces, Edges and Vertices of Cube
• Surface Area of Cuboid
• Surface Area of Cone
• Surface Area of Sphere

Examples on Unit Cube

Example 1: Find out the volume of a solid object which is made up by 16 unit cubes.

Solution:

As we know,

Volume of a Unit Cube is 1 unit³

Volume of 16 unit cubes = 16 × 1 unit³

Volume of 16 unit cubes = 16 unit³

Thus, required volume is = 16 unit³

Example 2: Length of side of a cube is 5 meter. Find the Volume of the cube.

Solution:

Volume of a Cube = side³

Volume of a Cube = 5³ cubic meter

Volume of a Cube = 125 cubic meter

Thus, required volume is 125 cubic meter

Example 3: A cube has 3 cm long diagonal, then find out the Volume of the cube.

Solution:

Using diagonal formula,

Volume of Cube = (√3 × Diagonal³)/9

Volume of Cube = (√3 × 3³)/9 cm³

Volume of Cube = 3√3 cm³

Therefore, required volume is 3√3 cm³

Example 4: Find out the surface area of a unit cube.

Solution:

Length of each side of a unit cube is 1 unit

Area of a side of unit cube = side × side = 1 unit²

Now,

Surface Area of a Unit Cube = 6 × 1 unit²

Surface Area of a Unit Cube = 6 unit²

Practice Problems on Unit Cube

P1: Find out the volume of a unit cube whose diagonal is √3 cm. ( in cm³)

P2: What is the surface area of a unit cube? (in unit²)

P3: What is the volume of an object which is made by 4 unit cubes?

P4: Find out the volume of a cube whose side length is 9 cm long.

Frequently Asked Questions On Unit Cube

What is a Unit Cube?

A unit cube is a cube with side 1 unit.

What is volume of a cube?

Volume of cube is the space occupied by the cube and its volume is calculated by the formula. V = a³

What are parts of a unit cube?

The parts of a unit cube are as follows:

• Six faces
• Twelve Edges
• Eight vertices

What is the curved surface area of a cube?

Curved Surface Area of Cube = 4 × side²

What is the total surface area of a cube?

Total Surface Area of Cube = 6 × side²

How many vertices does a cube have?

Cube has 8 vertices.