Perimeter, Area and Volume - Volume of Cube and Cuboid

Volume is the measure of the total space occupied by a three-dimensional object. While area measures the surface of a flat shape, volume measures the 'fullness' of a 3D shape, like how much water a tank can hold.

A Cuboid is a 3D figure with six rectangular faces. Visually, it looks like a shoebox or a brick, defined by three dimensions: Length ($l$), Breadth or Width ($b$), and Height ($h$).

A Cube is a special type of cuboid where all edges are of equal length. Visually, every face is an identical square. Think of a dice or a sugar cube as perfect examples where $length = breadth = height = side$ ($s$).

Volume is measured in cubic units. A cubic unit can be visualized as a small cube where each edge measures 1 unit (like $1\text{ cm}$ or $1\text{ m}$). Common units include cubic centimeters ($cm^{3}$), cubic meters ($m^{3}$), and cubic millimeters ($mm^{3}$).

The volume of a cuboid can be understood by 'layering.' If you calculate the area of the base ($length \times breadth$), and then multiply it by the number of layers (height), you get the total volume.

When calculating volume, ensure all dimensions are in the same unit. If the length is in $cm$ and the breadth is in $m$, convert the $m$ to $cm$ before multiplying ($1\text{ m} = 100\text{ cm}$).

Capacity is a term often used interchangeably with volume for liquids. For example, a container with a volume of $1,000\text{ cm}^{3}$ has a capacity of exactly $1\text{ liter}$.