Cube Formula: Full Explanation and Solved Examples

To get Circle Formula with examples from our best teachers. You can learn everything related to Cube formulas like Volume and Total Surface Area. A cube is a three-dimensional (3D) figure with six faces, eight vertices, and 12 edges. A cubic prism is a particular case.

A Cube

The Cube of a number instantly reflects the volume of a cube having an edge length equivalent to the given number. A cube is a 3-dimensional Figure composed of the same size as square-shaped faces. In a cube, all the angles meet at 90 degrees.

A cube has six identical faces of square shape and 12 equal edges, and eight vertices. Sometimes it is also known as a regular hexahedron or a square prism. In a cube the faces of a cube share a common border which is called the edge, which is considered the bounding line of the edge.

Some Examples of A Cube

There are some real-life examples of a cube are given below:

• A Rubik’s Cube
• A regular dice
• An ice cube etc.

Properties of A Cube

A cube is regarded as a remarkable kind of square prism in which all the faces of a cube are in the shape or figure of a square and are platonic solid. Like any other 3D or 2D form, a cube has many different properties. The properties of a cube are given below:

• Each vertex in a cube meets the three faces and edges.
•  In a cube, each of the faces meets the other four faces.
• A cube has 12 edges, six faces, and eight vertices.
• In a cube, the opposite planes or faces are parallel.
• In a cube, the opposing edges are parallel to each other.
• The angles of the Cube are right-angled.
• All 12 diagonals on the surface area of the same measure.

Cube Formula

The cubic formula helps us find a cube’s surface area, diagonal, and volume. The cube of a number directly represents the volume of the cube whose edge length is equal to the given number. A cube is a 3-D solid object consisting of six square faces with all sides of equal length. Let us finally learn about the cubic formula with some solved examples.

Some formulas related to the Cube will help us find diagonals, the surface area, and the volume of a cube. Now, Let us discuss the different formulas of a cube.

Surface Area of a Cube Formula

There are two (2) types of Surface Areas of the Cube:

1. Lateral surface area
2. Total surface area

1. Lateral Surface Area of a Cube Formula 

In a cube, the lateral area is the sum of the areas of all the side faces of the Cube. There are four side faces, so the summ of areas of all four side faces of a cube is its lateral area. The lateral area of Cube is also considered its (LSA)lateral surface area, and it is measured in square units.

The formula for the Lateral Surface Area of a Cube given below:

Lateral Surface Area of a Cube = 4a square

Here, a is the side length.

2. Total Surface Area of a Cube Formula 

In a cube, the total surface area is the sum of areaa of the cube’s vertical surfaces plus the base’s area. Therefore, In a cube, all the faces are made up of squares of the same dimension. Then, the total surface area of a Cube will add five times the surface area of one face five times.

The formula for Total Surface Area of a Cube given below:

Total Surface Area (TSA) of a Cube = 6a square

Here, a is the side length.

The volume of a Cube Formula

The volume of a cube is space occupied. It can find out by finding a Cube of the side length of a Cube. The importance of a cube has different formulas based on various parameters.

The different formulas for the Volume of a Cube are given below:

• The volume of the Cube (based on the diagonal) = (√3×d3)/9, 

Here d is the length of the diagonal of a cube.

• The Volume of the Cube (based on side length) = a3, 

Here a is the length of the side of a cube.

Diagonal of a Cube Formula

There are two different formulas related to the Diagonal of the Cube, which will help to find the length of diagonal of a cube. The different formulas for the Diagonal of a cube are given below:

• Length of a face diagonal of the cube = √2a units,

Here a = Length of each side of the Cube

• Length of main diagonal of the cube = √3.a units,

Here a = Length of each side of a cube.

Some Examples related to the Cube:

Example 1:

What amount of water is stored in one ice cube of side length 8?

Solution:

Given,

Length of the ice cube = 8 inches

Amount of water stored in the ice cube = the Volume of a Cube

Therefore, the volume of the ice-cube = 8 × 8 × 8 in3

= 512 in 3

Answer: The amount of water in ice is 512 in3.

Example 2:

Find the volume of Rubik’s Cube of length 15 inches.

Solution:

To find the volume of Rubik’s Cube:

The length of a side of cube= 15 in. (given)

Using the cube formula,

volume = s × s × s = s3

Put the values,

volume = 15 × 15 × 15 = 153 = 3375

Answer: The volume of Rubik’s Cube is 3375 cubic inches.

Example 3:

If the length of the side of a cube is 35 inches, find the total surface area.

Solution:

The Length of side of Cube, a = 35 inches.

Using the formula for area of a Cube, which is: A = 6a2

A = 6 × 35 × 35

A = 7350

Answer: The surface area of a Cube is 7350 square inches.

Extra Examples Related to the Cube:

Example 4:

Find the surface area of a cube having its sides equal to 14 cm in length.

Solution: 

Given that,

length = edge = 14 cm

We have,

The surface area of cube = 6 ( edge)2

                  = 6× 142

                  = 6 × 196

The surface area of the cube= 1176 cm2   

Answer: The surface area of a Cube is 1176 cm2 

Example 5:

The side of the cubic box is 18 m. Find the volume of a cubic box.

Solution:

Given,

Side = a = 18 m

By the formula of the volume of a cube, we know that

V = a3

V = 18 x 18 x 18

Volume = 5832 square meters or 5832 m2

Answer: The Volume is 5832 square meters or 5832 m2

Practice Questions Related to Cube:

1. What amount of water stored in one ice cube of side length 4?
2. Find the total surface area, if the length of side of a Cube is 13 inches.
3. The side of the cubic box is 19 m. Find the volume of a cubic box.
4. Find the importance of a Rubik’s Cube of length 23 inches.
5. Find a cube’s surface area with sides equal to 11 cm in length.
6. If the volume of a cube is 255 cm3, then what is the measure of the Cube’s edge?

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