Cube

Cube is a solid three-dimensional figure, which has 6 square faces or sides. We will discuss here its definition, properties and its importance in Maths. Also, learn the surface area and volume formula for the cube. 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.

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

  • Cuboid
  • Cylinder
  • Cone
  • Sphere

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 mentioned as a square parallelepiped, an equilateral cuboid and a right rhombohedron.

cube

 

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

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 learn its formula. The two major formulas are for surface area and volume of a solid shape.

  • Surface Area of Cube = 6a2 in a square unit
  • Volume of the cube = a3 in cubic units 

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

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 of Cube

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.

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