It is the amount of the space that an object and a substance occupy or that which is enclosed within a container. The most ideal approach to visualize volume is to consider it as far as the space enclosed/occupied by any 3-dimensional item or a solid shape.
We can see it by doing it at home,
- First, take a sheet of a paper, rectangular in shape length of 1cm and h cm of width.
- After that join the sides of the sheet as shown in the image below, without creasing the sheet.
- Then you will see that you have made 3-D object/shape, which encloses the space within.
Importance of the Volume
Units of the volume
It is given that volume has 3-D, it has a length of cubic measures.
Also, while the standard unit of measurement universally is a cubic meter or cubic centimetre, casually the most utilized term is litres or millilitres.
So, now we are fully familiar with the units of volume. Now, let’s take a look at calculating the volume of other common shapes and figures.
Cube
It is a special case of cuboid or we can say a rectangular prism, here all the three sides are equal when measured. When we represent a cube‘s side as ‘a’, then the cube has all the sides as ‘a’. Now, the volume a cube is calculated as;
Volume of cube=a x a x a = a³
Cylinder
A Cylinder shape is kind of tube-like structure with round outer faces of a similar span at either end joined by the planar circular surface.
Consider it the area of a circular increased by a 3rd-D, the height.
Volume of Cylinder = π x r x r x h = πr²h
Volume of Pyramid
The Pyramid shape formed by a base. It commonly is a triangle or a square. In spite of the fact that pyramids with bases with bigger than 4 are likewise conceivable and planar three-sided surfaces.
The volume of Pyramid = 1/3 x area of base x height
= 1/3 x a² x h
(here ‘h’ is the height of the Pyramid and a is the area of the base)
Volume of Cone
There is only one difference between a cone and a pyramid is that they both have different bases. The cone has the circular base and the pyramid has a squared base. Also, the pyramid has planar surfaces and the cone has a curved surface.
We can use ice cream cone as an example,
Volume of Cone = 1/3 x π x r x r x h
= 1/3 x π x r² x h
( so, h is the height of the cone and radius is denoted by ‘r’)
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