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Volume is a space occupied by any three-dimensional object. It is also a derived quantity that can be measured by measuring lengths.
The formula is written as,

$\begin{array}{l}\mathit{Volume}=\mathit{Length}×\mathit{Breadth}×\mathit{Height}\\ \\ =\mathit{Surface}\phantom{\rule{0.147em}{0ex}}\mathit{area}×\mathit{Height}\end{array}$

SI Unit

$\mathit{Volume}=l×b×h$

If the unit of volume is written in $$m$$, then

$$Volume$$ $$=$$ $$metre$$ $$×$$ $$metre$$ $$×$$ $$metre$$

$$=$$ $$cubic\ metre$$ or $$m^3$$

Hence, the SI unit of volume is a $$cubic$$ $$metre$$ (or) $$m^3$$.
The volume of regularly shaped objects
The volume of regularly shaped figures can be calculated using the relevant formula. Some of them are tabulated below.

 Shape Three-dimensional figure Volume Cube $\begin{array}{l}\mathit{side}×\mathit{side}×\mathit{side}\\ a×a×a={a}^{3}\end{array}$ Cuboid $\begin{array}{l}\mathit{length}×\mathit{breadth}×\mathit{height}\\ l×b×h\end{array}$ Sphere $\begin{array}{l}\frac{4}{3}×\mathrm{\pi }×{\left(\mathit{radius}\right)}^{3}\\ \frac{4}{3}\mathrm{\pi }{r}^{3}\end{array}$ Cylinder $\begin{array}{l}\mathrm{\pi }×{\left(\mathit{radius}\right)}^{2}×\mathit{height}\\ \mathrm{\pi }{r}^{2}h\end{array}$

Solved examples

1. Calculate the volume of a cube having sides of $$10\ m$$.

Sides, $$a\ = 10\ m$$

By substituting the known values on the formula of a cube, we get the following.

$\begin{array}{l}\mathit{Volume}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}a\phantom{\rule{0.147em}{0ex}}\mathit{cube}={a}^{3}\\ \\ =10×10×10\\ \\ =1000\phantom{\rule{0.147em}{0ex}}{m}^{3}\end{array}$

Therefore, the volume of a cube is $$1000\ m^3$$.

2. What will be the volume of a cylinder having a $$2\ m$$ radius and $$7\ cm$$ height?

Radius, $$r\ = 2\ m$$

Height, $$h\ = 7\ m$$

$\begin{array}{l}\mathit{Volume}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}a\phantom{\rule{0.147em}{0ex}}\mathit{cylinder}=\mathrm{\pi }×{r}^{2}×h\\ \\ =\frac{22}{7}×{\left(2\right)}^{2}×7\\ \\ =88\phantom{\rule{0.147em}{0ex}}{\mathit{cm}}^{3}\end{array}$

Therefore, the volume of a cylinder is $$1000\ cm^3$$.
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