Cube and its surface area

## Objective

To form a cube and find the formula for its surface area.

### What is a cube ?

A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. (Refer Fig: 1) Fig.(1) Square

### Surface area of cube (Refer Fig: 2)-

• The surface area of any three-dimensional shape is the total region covered by all its faces.
• In the same way, the surface area of a cube is the sum of the areas of all its six square faces.
• All six faces of the cube are made up of squares of the same dimensions then the total surface area of the cube will be the surface area of one face added six times to itself.
• The formulas for these can be derived from the figure given below. Fig.(2) Cube Net

### Total surface area of cube formula -

• Length of the side of the cube = a units
• Area of one square = a² sq.units
• Sum of the area of all the squares = ( a² + a² + a² + a² + a² + a² ) sq.units
• Therefore, surface area of cube = 6 x a² sq.units