Cube

In Maths or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron. You must have seen 3 × 3 Rubik’s cube, which is the most common example in the real-life and it is helpful to enhance brainpower. In the same way, you will come across many real-life examples, such as 6 sided dices, etc. We will discuss here its definition, properties and its importance in Maths. Also, learn the surface area formula for the cube along with its volume formula.

Solid geometry is all about three-dimensional shapes and figures, which have surface areas and volumes. The other solid shapes are;

  1. Cuboid
  2. Cylinder
  3. Cone
  4. Sphere

Table of contents:

Cube Definition

As discussed earlier, a cube is a 3-D solid shape, which has 6 sides. Along with that, it has 8 vertices and 12 edges such that 3 edges meet at one vertex point. Check the given image below, defining its faces, edges and vertices. It is also known as a square parallelepiped, an equilateral cuboid and a right rhombohedron.

cube

In the above figure, you can see, edge, face and vertex of the cube. Here, L stands for length, B stands for breadth and H stands for height. We can see, the length, breadth and height of the cube, which represents the edges of the cube, connects at a single point which is the vertex. The faces of the cube is connected by four vertices.

Now let us discuss in brief its properties in this article, along with the formula for surface area and volume.

Surface Area and Volume Formula For Cube

We have discussed until now the definitions and properties of the cube along with its importance in solid geometry. Now let us see the two major formulas for a solid shape, i.e. surface area and volume.

Surface area of Cube

We know that for any shape, the area is defined as the region occupied by it in a plane. A cube is a three-dimensional object, therefore, the area occupied by it will be in 3d plane. Since a cube has six faces, therefore, we need to calculate the surface area of the cube, covered by each face. Hence, the formula for surface area is given by:

  • Surface Area of Cube = 6a2 in a square units

Volume of Cube

The volume of the cube is the space contained in it. Suppose, if an object is in cubical shape and we need to immerse any material in it, say water, then the measure of waters in litres to be kept in the object is calculated by its volume. The formula of the volume is given by:

  • Volume of cube = a3 cubic units

Length of Diagonal of Cube

If a is the length of the side, then,

  • Length of Diagonal of Face of the Cube = √2 a
  • Length of Diagonal of Cube = √3 a

Also, see:

Properties of Cube

  1. It has all its faces in a square shape.
  2. All the faces or sides have equal dimensions.
  3. The plane angles of the cube are the right angle.
  4. Each of the faces meets the other four faces.
  5. Each of the vertices meets the three faces and three edges.
  6. The edges opposite to each other are parallel.

Examples

1. If the value of the side of the cube is 10cm, then find its surface area and volume.

Solution:

Given, side , a = 10cm

Therefore, by the surface area and volume formula of the cube, we can write;

Surface Area = 6a2 = 6 × 102 = 6 × 100.= 600 cm2

Volume = a3 = 103 = 1000 cm3

Learn more about different geometrical shapes and figures here at BYJU’S. Also, download its app to get a visual of such figures and understand the concepts in a better way.

3 Comments

  1. It’s very useful for everyone. Thank you

  2. Thank for mathmetic properties help and I memerized deeply

  3. I want 10 examples of cube, can anyone please tell me?

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