Why Volume of a Cube is a3

Volume 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.

Cube

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, the base of the cube is in the form of square with side aand also the height of the cube is aas shown in figure below.
  • The space occupied by the cube is called as the volume of the cube.

  • The volume of the cube is given by,

Volume of cube = base area*height of the cube

 

But the base of the cube is in the form of square with side a, then we know that area of square is given by,

Area of square base of the cube = side 2 = a2

Hence, the volume of the cube is given by,

Volume of the cube = base area*height of the cube

= a2*a

 

Thus, the volume of cube of cube length a is given by,

Volume of the cube = a3 (Hence proved.)


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