### Theory:

Length is one of the fundamental quantity that cannot be conveyed in any other way. Other measurements, such as area and volume, can be calculated using length.

**Area**

In general, two lengths are used to calculate the area of an object.

The formula is given as,

$\begin{array}{l}\mathit{Area}=\mathit{Length}\times \mathit{Breadth}\\ =l\times b\end{array}$

By using the above formula, the area of a book, house or even a garden can be found. The SI unit for the area of a surface is \(m^2\) since it is a product of two lengths.

**Example**:

Assume the length and breadth of the wall are \(20\ m\) and \(8\ m\), respectively. Then, what will be the area of the wall?

Length of the wall \(=\) \(20\ m\)

Breadth of the wall \(=\) \(8\ m\)

$\begin{array}{l}\mathit{Area}=l\times b\\ =20\phantom{\rule{0.147em}{0ex}}\times \phantom{\rule{0.147em}{0ex}}8\\ =160\phantom{\rule{0.147em}{0ex}}{m}^{2}\end{array}$

Therefore, the area of the wall is \(160\) \(m^2\).

**Volume of solids**

A volume is the amount of 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,

$\mathit{Volume}=\mathit{Length}\times \mathit{Breadth}\times \mathit{Height}$

The SI unit of volume is a \(cubic\) \(metre\) or \(m^3\).

**Calculation of volume of a solid box**

A volume of a solid box can be found using three parameters such as length (\(l\)), breadth (\(b\)) and height (\(h\)). These parameters are measured using a measuring scale in terms of \(cm\) or \(m\).

$\mathit{Volume}=l\times b\times h$

If the unit of volume is written in \(cm\), then

\(Volume\) \(=\) \(centimetre\) \(×\) \(centimetre\) \(×\) \(centimetre\)

\(=\) \(cubic\ centimetre\) or \(cm^3\)

**Example**:

Look at the image of the solid box and calculate its volume.

The dimensions of the solid box are given below:

Length, \(l\ = 10\ cm\)

Breadth, \(b\ = 10\ cm\)

Height, \(h\ = 10\ cm\)

Length, \(l\ = 10\ cm\)

Breadth, \(b\ = 10\ cm\)

Height, \(h\ = 10\ cm\)

$\mathit{Volume}=l\times b\times h$

By substituting the known value on the formula, we get the following.

$\begin{array}{l}\mathit{Volume}=10\times 10\times 10\\ =1000\phantom{\rule{0.147em}{0ex}}{\mathit{cm}}^{3}\end{array}$

If the volume of a solid cubical box is \(1000\ cubic\ cm\), then it means that \(1000\) cubes, each with dimensions \(1 cm\) \(×\) \(1 cm\) \(×\) \(1 cm\), can be placed inside the box.