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Cube – Definition, Shape & Formula: A Cube is a solid or hollow three-dimensional form of a square that has six square faces, eight vertices, and twelve edges. Some examples of cubes that we see regularly are sugar cubes, ice cubes, Rubik’s cubes, etc. The length, breadth, and height of a cube are the same as each face of a cube is a square. A cube is also known as an equilateral cuboid, a square parallelepiped, or a right rhombic hexahedron and is one of the five platonic solids. In this article, we will discuss what is a cube, cube shape, formulas related to cubes, properties, and examples. Table of Content What is a Cube in Maths?Cube is a 3D solid shape with six square faces with all 12 sides of equal length. A cube can be considered a special cuboid where all the length, breadth, and height are equal. A cube is a special case of a square prism having six square faces, eight vertices, and twelve edges. We see various shapes in our daily lives that resemble the cube. Such as a 3×3 Rubik’s Cube a puzzle famous among many, is an example of a cube. The image added below shows a cube along with its faces, edges, and vertices. Cube Definition in Maths
Studying, the above figure, we conclude that two faces of cube have a common boundary called edge of cube and there are twelve (12) edges of cube, similarly on observing figure closely we conclude that a cube has six (6) faces and eight (8) vertices. Cube ShapeCube shape is one of the fundamental shapes of mathematics and is observed very often in our daily lives. We can assume the cube is a polyhedron with equal length, breadth, and height. It can be easily stacked on one over another without leaving any spaces. We say about a cube that,
We see various types of figures in our daily life that are shaped like cubes that include, boxes, ice cubes, sugar cubes, etc. Cube ExamplesVarious Cube Examples are shown in the image below:  Cube Examples Properties of CubeA cube is a 3D figure with equal dimensions having various properties. Some of the properties of the cube are,
Faces, Edges and Vertices in Cube
Cube Faces
Cube Edges
Cube Vertices
Euler’s Formula in CubeEuler’s Formula gives the relation between Faces, Edges and Vertices of a Polyhedron. Let’s verify the same for a cube. According to Euler’s Formula we know that
In a cube, F = 6, V = 8 and E = 12. Putting this value in above expression we get
Thus, cube satisfies Euler’s Formula Net of CubeA cube is a 3-D figure and a figure in 2-D that can be folded easily to form the cube is called the net of a cube. Thus, we can say that the two-dimensional form of a cube that can be folded to form a three-dimensional form is called a net of a cube. There are various ways to unfold a cube, i.e. a cube can have various nets one of nets of cube is discussed in image below,
Cube FormulaThere are various formulas that are helpful to find various dimensions of cube, that include length of its diagonal, its surface area, its volume, etc. various cube formulas discussed in article are, Now let’s learn about these formulas in detail. Diagonal of CubeDiagonal of a cube is the line segment that joins the opposite vertices of the cube. A cube has two types of diagonals, i.e., a face diagonal and a main diagonal. A face diagonal is a line that joins the opposite vertices of the face of a cube and is equal to the square root of two times the length of the side of a cube. As the cube has six faces, it has a total of 12 face diagonals. The formula to calculate the face diagonal of the cube is,
where, a is Length of Side of a Cube While the main diagonal is the line segment that joins the opposite vertices, passing through the center of the cube, and is equal to the square root of three times the length of the side of a cube. A cube has a total of four main diagonals.
where, a is Length of Side of a Cube Below image represents main diagonal and face diagonal of cube.
Surface Area of a CubeArea of any object is space occupied by all the surfaces of that object. It can be defined as the total surface available for the painting. A cube has six faces and so its surface area is calculated by finding the area of the individual face and finding its sum. There are two types of surface area associated with a cube that are mentioned below,
Lateral Surface Area of CubeLateral Surface Area of a cube is the sum of the areas of all the faces of a cube, excluding its top and bottom. In simple words, the sum of all four side faces of a cube is the lateral surface area of a cube. It is measured in square units such as (units)2, m2, cm2, etc. Formula for the lateral surface of a cube is
where, a is Length of Side of a Cube Total Surface Area of CubeTotal Surface Area of a cube is the space occupied by it in three-dimensional space and is equal to the sum of the areas of all its sides. It is measured in square units such as (units)2, m2, cm2, etc. Formula for the total surface of a cube is
where, a is Length of Side of a Cube Volume of CubeVolume of a cube is the amount of space enclosed by the cube. It is usually measured in terms of cubic units. It is measured in cube units such as (units)3, m3, cm3, etc. Formula for the volume of a cube is
where, a is Length of Side of a Cube We can also calculate the volume of the cube if its diagonal is given, by using the formula,
where, d is Length of Main Diagonal of Cube Cube – Important FactsThe various important facts related to cube are mentioned below:
People Also Read:Cube ExamplesExample 1: Find the total surface area of a cube if the length of its side is 8 units. Solution:
Example 2: Find the volume of a cube if the length of its side is 5.5 inches. Solution:
Example 3: Find the length of the diagonal of a cube and its lateral surface area if the length of its side is 6 m. Solution:
Example 4: Determine the length of the diagonal of the cube if the volume of the cube is 91.125 cm3. Solution:
Example 5: Determine the volume of the cube if its total surface area is 54 square units. Solution:
Example 6: Find the lateral surface area and the total surface area of a cube if the length of its diagonal is 5√3 units. Solution:
Example 7: Find the length of the side of a cube if its lateral surface area is 196 square inches. Solution:
Practice Questions: Cube – Definition, Shape & FormulaTry out following practice questions on Cube Formula
Conclusion of CubeThe cube is a geometric shape that has intrigued mathematicians, engineers, and artists for centuries. Its symmetrical properties and uniformity make it a versatile and practical tool in various fields, from architecture to mathematics. By understanding the properties and applications of cubes, we gain insight into the world of geometry and its relevance in everyday life. So, whether you’re building structures, solving puzzles, or exploring mathematical concepts, the cube remains an essential and intriguing element to study and appreciate. What is Cube – FAQsWhat is a Cube?
What are Five Examples of Cube?
How Many Faces, Edges and Vertices are in Cube?
What is the difference between a Cube and a Cuboid?
What is the Formula to Calculate the Surface Area of a Cube?
What is the Formula to Calculate the Volume of a Cube?
What are Cube Edges?
How do You Find Vertex of a Cube?
What is Cube Formula?
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