What Is a Cube Shape Definition Properties Surface Area and Volume Formula with Examples
In Euclidean Geometry, a cube is a regular solid shape with six square faces, twelve edges, and eight vertices. A cube is also said to be a regular hexahedron or square prism as all its faces are square in shape. The dimensions i.e. the length, breadth, and height of a cube are equal. An ice cube, Rubik’s cube, and dice, etc. are some of the real life examples of a cube. Read on to know more about geometric cube in detail.
Cube Definition in Maths
A cube is defined as a three dimensional solid object that has six identical square faces. The six identical square faces of a cube meet each other at right angles.
The cube, also known as regular hexahedron, is one of the five platonic solid objects. It has 6 faces, 12 vertices, and 8 edges.
Cube Shape Examples
Here are some of the real-life examples of a cube which are mostly observed in everyday life.
Ice Cubes
Dice
Sugar Cube
Rubik Cube
Cube Building Blocks
Chocolate Cube
Cube Diagram
The following cube diagram shows 6 square faces, 12 vertices, and 8 edges.
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Parts of Cube Shape Diagram
The description of the cube shape parts are as follows:
Face: A cube has six flat faces, or surfaces. The face of a cube is also referred to as facets or sides. Each cube faces are square in shape. Among six faces of a cube, each and every face has four equal sides. The sides of each cube face are known as edges.
Edge: The edge of a cube is a line segment joining two vertices. There are 12 edges of a cube. All the 12 edges of a cube are equal in length because the all six faces of a cube are square in shape.
Vertex: A point where three edges meet is known as vertex. There are a total of 8 vertices in a cube.
Properties of Cube
A cube has 6 faces , 8 vertices, and 12 edges.
As all the faces of a cube are square in shape, therefore, the length, breadth, and height of a cube are equal.
The angle between any two sides of a cube is 90 degrees.
Each face of a cube meets the other four adjacent faces.
The opposite sides of a cube are equal and parallel to each other.
The vertex of a cube is a point where two or more edges meet.
Cube Formulas
The following cube formulas help you to calculate the volume and surface area of the cube.
Volume of Cube
The volume of a cube is defined as the total number of cubic units required to fill the given cube completely.
Units of Volume of Cube includes:
Metric: Cubic meters (m), cubic centimeters (cm), liters, etc.
US Standard Unit: Cubic inch, Cubic foot, pints, gallons, etc.
The formula for finding the volume of cube is given as:
The volume of the cube can also be found using the diagonals of a cube. The volume of cube formula using the diagonals of a cube is given as:
Surface Area of Cube
Here, we will learn how to find total surface and lateral surface area of cube using formulas:
Total Surface Area of Cube
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The total surface area of a cube is the sum of the areas of its six faces or sides.
Look at the cube given above. Each of the six faces of the cube is square in shape.
As faces are square, therefore, area of each face = a2
Total surface area (TSA) of a given cube = a2 + a2 + a2 + a2 + a2 + a2
Therefore, TSA = 6a2
Lateral Surface Area of Cube
The lateral surface area of a cube is the sum of the areas of all its faces excluding the top and bottom.
Therefore, the lateral surface area of a cube is given as 4a2
Solved Examples
1. Find the total surface area of the cube of side length 5 cm.
Solution:
Total Surface Area (TSA) = 6a2
Given side length 5 cm, the total surface area of the cube is calculated as
TSA = 6(5)2
TSA = 6 52
TSA = 150 cm2
2. Find the volume of the cube with side length 9 cm.
Solution:
As we know,
Volume of cube = (side)
Here, side length = 9 cm
= 9 9 9
= 729 cm3
Therefore, the volume of cube = 729 cm3
3. Find the lateral surface area of the cube if the length of the side of the cube is 7 cm.
Solution:
Lateral Surface Area (TSA) = 4a2
Given side length 5 cm, the total surface area of the cube is calculated as
LSA = 4(7)2
LSA = 4 72
LSA = 196 cm2
Cube Related Facts
FAQs on Cube Shape Explained with Properties and Formulas
1. What is a cube shape in maths?
A cube is a three-dimensional solid shape with 6 equal square faces, 12 equal edges, and 8 vertices. It is a special type of cuboid where all edges have the same length. In geometry, a cube is also called a regular hexahedron. Everyday examples include dice, ice cubes, and Rubik’s cubes.
2. What are the properties of a cube?
A cube has fixed geometric properties that make it a regular 3D shape. The key properties of a cube are:
- 6 square faces
- 12 equal edges
- 8 vertices
- All interior angles are 90°
- All faces are congruent squares
Because all sides are equal, a cube is both a prism and a Platonic solid.
3. What is the formula for the volume of a cube?
The volume of a cube is calculated using the formula V = a³, where a is the length of one edge. Since all sides are equal, you multiply the side length by itself three times.
- If a = 4 cm
- V = 4 × 4 × 4 = 64 cm³
Volume is measured in cubic units such as cm³, m³, or in³.
4. How do you find the surface area of a cube?
The surface area of a cube is given by the formula 6a², where a is the side length. This works because a cube has 6 identical square faces.
- Area of one face = a²
- Total surface area = 6 × a²
- If a = 5 cm, surface area = 6 × 25 = 150 cm²
5. What is the difference between a cube and a cuboid?
The main difference is that a cube has all edges equal, while a cuboid has edges of different lengths.
- Cube: length = breadth = height
- Cuboid: length, breadth, and height may differ
- Volume of cube = a³
- Volume of cuboid = l × b × h
A cube is a special case of a cuboid where all dimensions are the same.
6. How many edges, faces, and vertices does a cube have?
A cube has 6 faces, 12 edges, and 8 vertices. Each face is a square, and three edges meet at each vertex. These values satisfy Euler’s formula for polyhedra: V − E + F = 2, since 8 − 12 + 6 = 2.
7. What is the diagonal of a cube formula?
The space diagonal of a cube is given by the formula d = a√3, where a is the side length. This diagonal connects two opposite vertices inside the cube.
- If a = 6 cm
- d = 6√3 cm
This formula is derived using the Pythagorean theorem in three dimensions.
8. Can you give an example of solving a cube problem?
To solve a cube problem, use the appropriate formula based on what is asked.
- Given side length a = 3 m
- Volume = a³ = 3³ = 27 m³
- Surface area = 6a² = 6 × 9 = 54 m²
This shows how cube formulas are applied directly once the side length is known.
9. Why is a cube called a regular solid?
A cube is called a regular solid because all its faces are identical regular polygons and all angles are equal. It is one of the five Platonic solids. Each face is a square, and the same number of faces meet at every vertex, making it perfectly symmetrical.
10. Where is the cube shape used in real life?
The cube shape is commonly used in everyday objects and design because of its symmetry and stability. Examples include:
- Dice used in games
- Ice cubes
- Storage boxes
- Building blocks and packaging
In mathematics and geometry, cubes are used to understand volume, surface area, and three-dimensional measurement.
