Proof of Surface area of a Cube

Surface area of a Cube

  • Cube is the three-dimensional object as shown in figure which is special cuboid having length, breadth and height all in equal magnitude. Hence cube has 6 square surfaces, 8 vertices or corners, 12 edges and 4 diagonals as shown in figure.

Derivation for Surface area of Cube:

  • As we know that, cube has 6 square surfaces as shown in figure. Let us consider cube with side having length a then to find the surface area of cube we have to add the surface area of all 6 square surfaces.
  • The following figure shows the cube having side length a. when we open the cube totally then it looks like the structure shown in figure below.
  • We know that, the surface area of square = side2 = a2
  • But cube has total 6 square surfaces so total surface area of cube will be the sum of all 6 square faces of cube.

Total surface area of cube = sum of surface area of all 6 square surfaces of cube

= 6*a2

Thus,

The surface area of cube having side length a is given by,

Surface area of cube = 6*a2

Hence proved.


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