It is the amount of space an object and a substance occupy or is enclosed within a container. The ideal approach to visualize volume is considering 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 paper, rectangular in shape, length of 1cm and h cm in 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 a 3-D object/shape enclosing the space within.
Key Takeaways
- Volume is the amount of space occupied by an object, measured in cubic units.
- Volume is essential in engineering, physics, and chemistry, where it calculates density, mass, and pressure.
- The volume of a solid object can be calculated by multiplying its length, width, and height, while for a liquid, it is measured in milliliters or liters.
Importance of the Volume
Units of the volume
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 calculate the volume of other common shapes and figures.
Cube
It is a special case of a cuboid or a rectangular prism; here, all three sides are equal when measured. When we represent a cube’s side as ‘a’, the cube has all the sides as ‘a. Now, the volume of a cube is calculated as;
Volume of cube=a x a x a = a³
Cylinder
A Cylinder shape is a tube-like structure with round outer faces of a similar span at either end joined by a planar circular surface.
Consider it the area of a circular increased by a 3rd-D, the height.
The volume of the Cylinder = π x r x r x h = πr²h
Volume of Pyramid
A base forms a Pyramid shape. It is commonly a triangle or a square, even though pyramids with bases bigger than 4 are likewise conceivable and planar three-sided surfaces.
The volume of the 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 a 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 cones as an example,
The 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 the radius is denoted by ‘r’)
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