Volume

Definition of Volume:
This is a quantity of measurement of space inside a three dimension closed surface.This is usually noted by the alphabet "V" and sometimes "Vol".

 To get a better understanding about vol., we can consider the two closed surface like rectangular prism and cube.

Let us consider a closed rectangular box. In math, it is said  to be as closed rectangular prism. For any rectangular prism, each  of the face would be  rectangle. To find the vol ume(V) of a rectangular prism, we need to have the three measurements. They are length ,width of the base then height of the prism. Once we have these three measurements, we can easily find the vol. of rectangular prism.

Method of finding vol. of a rectangular prism:

Vol. of rectangular prism = (Base area)X(Height)

Here area of the base can be found by using the length and width of the rectangle that we have at the base.

Area of the base=length X height

Here to find the area of the base, we have used the formula of area of rectangle. Because each face of rectangular prism would be a rectangle. So the base also must be a rectangle. So to find the area of the base, we use area of the rectangle that is length times width.

Hence, vol. of any rectangular prism is = (Length)X(Width)X(Height)

Volume of cube:

Let us consider a cube. For any cube, each face would be a square.And we already know that all the four sides of square would be equal.To find the vol. of any cube, we have to know the three measurements as we did in rectangular prism. They are length and width of the base then height of the cube. Once we know these three measurements, we can easily find the vol. of any cube.

But here all these three measurements would be equal. Because each face is a square.  

Vol. of cube = (Base area)X(Height)

Here area of the base can be found by using the length and width of the square that we have at the base.

Area of the base=length X height

If "a" be the length of each side of a square, then the area  of the base is = a²

Here to find the area of the base, we have used the formula of area of square. Because each face of cube would be a square. So the base also must be a square. So to find the area of the base, we use area of the square that is side times side.

Hence, volume of any cube is = (Side)X(Side)X(Side)
                                                        = a X a X a
                                                        = a³