Question

What is the dimension formula of volume?

Answer 1

Step 1: Definition

The quantity of space occupied by a thing, whereas capacity seems to be the ability of an object to contain a material, such as a solid, liquids, or gaseous is called volume.

Step 2: Dimensional formula

We know the formula of volume,

$\mathrm{Volume}\left(\mathrm{V}\right)=\mathrm{Length}\times \mathrm{breadth}\times \mathrm{height}$…(equation $1$)

The dimensional formula of length is:

$\left[{\mathrm{M}}^0{\mathrm{L}}^1{\mathrm{T}}^0\right]$ …(equation $2$)

By substituting the equation $2$ in the equation $1$ we get,

$\mathrm{V}=\left[{\mathrm{M}}^0{\mathrm{L}}^1{\mathrm{T}}^0\right]\times \left[{\mathrm{M}}^0{\mathrm{L}}^1{\mathrm{T}}^0\right]\times \left[{\mathrm{M}}^0{\mathrm{L}}^1{\mathrm{T}}^0\right]=\left[{\mathrm{M}}^0{\mathrm{L}}^3{\mathrm{T}}^0\right]=\left[{\mathrm{L}}^3\right]$

Therefore, the dimensional formula of volume will be $\left[{\mathrm{L}}^3\right]$.