Question

What is the formula for the total surface area of a cube?

Answer 1

Hint: In this particular type of question use the concept that all the sides in a cube are equal and the cube has a total 6 face which resembles a square so the total surface area of a cube is 6 time the area of a square so use these concepts to reach the solution of the question.

Complete step by step solution:

Let us consider a cube ABCDEFGH as shown in the above figure.
There are six face in a cube which are given as,
ABCD, ABGE, CDFH, AEFD, BCGH and EFHG.
Now as we know that in a cube all the sides are equal.
So let side AD be a unit.
Therefore, AD = AB = BC = CD = AE = DF = BG = CH = EF = FH = HG = GE = a units.
So each face of the cube resembles a square.
Now as we know that the area of the square is calculated as the square of the side.
So the area of the square ABCD = ${\left( {{\text{side}}} \right)^2} = {a^2}$ sq. Units.
So the area of all the faces is the same as the side of the square is the same.
So as there are 6 faces in the cube so the total surface area of the cube is 6 times the area of the square.
So the total surface area of the cube = $6{a^2}$ sq. Units.
So this is the required total surface area of the cube.
So this is the required answer.

Note: Whenever we face such types of questions the key concept we have to remember is that always recall the formula of the area of the square which is the basis to find the total surface area of the cube so first find out that there are how many faces in the cube then multiply the area of the square to the number of faces of the cube which is the required surface area of the cube.