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Derivation of Volume of Cube

Cube:
A three-dimensioned solid cuboid whose length,breadth and height are all equal is called a cube. 


A Cube

Cube is  combination of vertex,Edge,Faces 
Vertex: is point , where two or more lines meet(8).
Edges: Edges is the line of the cube (12).
Faces:the views of the object is called as Faces (6).

Vertex Edges

Volume:
The amount of space occupied by a three dimensional object is called as volume. volume of room is greater than volume of an match box. cubic unit are used to measure the volume of solid objects. 

Volume of cube:
Measurement of volume is carried in cubic units whereas the area of region or surface s are measured in square units.

How to find the volume of cube/derivation

By measuring one side of the cube and cubing the length of the one side gives the volume.
                                     (or)

Multiplying the length,width and the height of the cube gives the volume of cube.
                                 V = l*h*w
In general volume of cube is side*side*side. Thus
                                V = l*l*l
                                   = l3

Example:

         1.Find the volume of cube whose sides of equal length of 5m.

         Solution:

         Given that the length of each side is 5. This means length,height and  width of  equal measurement.
         Step1: volume of cube = l*h*w
         Step 2: (assign the value )              = 5 x 5 x 5
         Step 3:  Simplify       = 25 x 5
                                                                              = 125 m3

          2. Calculate the Volume of cube which side a is 9m.

          Solution:

          Given that the length of each side is 9.

          Step1:       volume of cube = l*h*w
          Step 2: (assign the value )                     = 9 x 9 x 9
          Step 3:  Simplify              = 81x 9
                                                                                     = 729 m3