We will discuss here cube along with its definitions, formulas, properties and its importance in Maths. The cube is basically defined in solid geometry section. Solid geometry is all about three-dimensional figures, which have surface areas and volumes.
Similarly, a cube is also a solid three-dimensional figure, which has 6 square faces or sides. The properties of cubes vary with other types of solid figures such as;
We can define a cube as a rectangular solid, which has 6 faces of same length, breadth and height. Also, it has 8 vertices and 12 edges such that 3 edges meet at one vertex point. Check the given diagram for the cube, defining its faces, edges and vertices.
The cube is also mentioned as a square parallelepiped, an equilateral cuboid and a right rhombohedron.
Now let us discuss in brief the properties of the cube in this article, along with formulas of its surface area and volumes.
Formulas for Cube
We have discussed until now the definitions and properties of the cube along with its importance in solid geometry. Now let us learn the formulas of the cube. The two major formulas for the cube is to find the surface area and volume of a cube.
The area of the surface of a cube or the outer side of a three-dimensional shape is called a Surface area of cube and is measured in square units, like m2, cm2, etc. Suppose a is the length of sides of the cube, then the formula for surface area of the cube can be represented as;
Surface area of a cube = 6 times of side2 = 6 × side2
Surface Area of Cube = 6a2 in a square unit
Similarly, the volume of a cube is defined as the space occupied by the cube and is measured in cubic units such as m3, cm3, etc. The formula for the volume of the cube can be represented as;
Volume of the cube = side × side × side = side3
Volume of the cube = a3 in cubic units
Properties of Cube
- Cubes have all the faces in a square shape.
- All the faces or sides of the cube have equal dimensions.
- The plane angles of the cube are the right angle.
- Each of the faces meets the other four faces.
- Each of the vertices meets the three faces and three edges of the cube.
- The edges opposite to each other in a cube are parallel.
- If a is the length of the side of the cube, then,
Length of Diagonal of Face of the Cube = √2 a
Length of Diagonal of Cube = √3 a
Example: If the value of the side of the cube is 10cm, then find the surface area and volume of the cube.
Solution: Given, the value of side of cube, a = 10cm
Therefore, by the surface area and volume formula of the cube, we can write;
Surface Area of Cube = 6a2 = 6 × 102 = 6 × 100.= 600 cm2
Volume of the cube = a3 = 103 = 1000 cm3
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