Question

If the length of the diagonal of a cube is 4cm then let us calculate total surface area

Answer 1

Solution:

Given: The length of the diagonal of a cube is 4 cm

To find: Total Surface Area of the cube.

Let us consider  a dimension of the cube(a square).

A              B
l------------l
l           /   l
l       /       l
l   /           l
l----------Γl
C          D
In Δ BCD,
∠D=90°
Hence,Δ BCD is right angled triangle.
CD=BD=4  (length of a dimension of a cube(a square) are equal)


The diagonal of the square (by pythagoras theorem): √a²+a² =√2a²=   a√2 cm.

The top dimension of the cube(where we can use diagonal as base) will have:
                  The diagonal of top dimension of the cube= dimension of cube          

                                                   4  = √a²+(a√2)²
                                                   4  =√a²+2a²
                                                   4  =√3a²
                                                   4  =a√3
                                               4/√3 =a,.
we know that,TSA of cube = 6a²
                                               = 6(4/√3)
                                               =3 x 2 x(4/√3)
                                               =√3 x √3 x 2 x (4/√3)
                                               =√3 x 2 x4
                                               =8√3 cm²