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The space occupied by any object is its volume, and volume is used to compare different things around us.
For example, the volume of a CPU is greater than the volume of a mouse pad. Also, the volume of a bookshelf is greater than the volume of the book kept inside it.
The volume of objects is expressed in cubic units.
Let us now learn to calculate the volumes of different \(3\)-D solids.
The volume of a cuboid
The product of all three dimensions of a cuboid is its volume.
Therefore, \(\text{The volume of a cuboid} = \text{Length} \times \text{Breadth} \times \text{Height}\).
It can also be written as \(\text{The volume of a cuboid} = \text{Area of the base} \times \text{Breadth}\).
[Since, \(\text{Area of the base} = \text{Length} \times \text{Height}\)]
The volume of a cube
In a cube, all sides are equal.
The volume of a cube can be derived from the formula to find the volume of a cuboid.
\(\text{The volume of a cuboid} = \text{Length} \times \text{Breadth} \times \text{Height}\)
Since all sides in a cube are equal, we should substitute \(\text{Length}\) in the place of \(\text{Breadth}\) and \(\text{Height}\).
Thus, \(\text{The volume of a cube} = \text{Length} \times \text{Length} \times \text{Length} = (\text{Length})^3\)
Volume of a cylinder
A cylinder has two dimensions, namely radius and height.
\(\text{The volume of a cylinder} = \text{The area of the base} \times \text{Height}\)
\(= \pi \times r^2 \times h\)
[Since the base of a cylinder is a circle, \(\text{the area of the base} = \pi r^2\)]
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