Surface Areas and Volumes - Volume of a Cuboid and Cube

Volume refers to the amount of three-dimensional space occupied by an object. Visually, you can think of volume as the number of unit cubes (cubes with side $1$ unit) that can fit perfectly inside a solid without leaving any gaps.

A cuboid is a solid figure bounded by six rectangular faces. Visually, it has three distinct dimensions: length ($l$), breadth ($b$), and height ($h$). Imagine a rectangular shoe box; the area of the base is $l \times b$, and when you stack multiple such rectangular layers up to a height $h$, you get the volume.

A cube is a special case of a cuboid where all three dimensions are equal. Visually, every face of a cube is a square of the same size. If the edge length is $a$, then the length, breadth, and height are all equal to $a$.

The volume of any right prism (like a cuboid) is calculated as the Area of the Base multiplied by the Height. For a cuboid, the base is a rectangle ($Area = l \times b$), so the Volume becomes $Area \times h = l \times b \times h$.

Capacity is a term used for the volume of a substance (liquid or gas) that a hollow container can hold. While volume usually refers to the space occupied by the solid material itself, capacity refers to the internal space available for storage.

Units of volume are derived from linear units and are expressed as cubic units. Common units include $cm^3$ (cubic centimeters), $m^3$ (cubic meters), and $mm^3$. For liquids, we use Litres ($L$) and Millilitres ($mL$).

Conversion between units is crucial: $1$ cubic meter ($m^3$) is equal to $1,000,000 cm^3$. In terms of liquid capacity, $1000 cm^3 = 1 L$ and $1 m^3 = 1000 L$. This means $1 cm^3$ is equivalent to $1 mL$.