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# Converting Area and Volume Units

### Converting Area and Volume Units

We measure area and volume in units with indices, as they contain multiple dimensions that we need to account for.

We use units with indices to measure area and volume as there are extra dimensions which we need to account for.

Remember that area of a square is calculated by multiplying the length of two sides together.

The area of a square is measured by multiplying the two side lengths

See the image

When we record area, it is given in **square** units. This is because we need to account for the length and height dimensions. Often we use **square centimetres** -$cm^2$- or square metres -$m^2$. But how many square centimetres are in a square metre?

As there are **100cm** in **1m**, it can be easy to think there are $100cm^2$ in $1 m^2$; but this isn't correct. A square metre is:

$100cm \times 100cm = 10000cm^2 = 1m^2$

Here is a visual representation of the area in centimetres

Note the unit used for area

How many square centimetres are there in 2 square metres?

A similar approach can help us understand how many square metres in a square kilometre.

There are $1000m$ in a kilometre.

How many $m^2$ are there in a square kilometre?

How many square metres are there in 4 square kilometres?

Volume is measured in cubic units, often cubic centimetres - $cm^3$ - or cubic metres - $m^3$.

If we consider a $1m^3$ cube we can calculate how many $cm^3$ in $1m^3$.

The calculation for volume of a cube

Notice the units used for volume

How many cubic centimetres are there in 3 cubic metres?

Similarly: $100mm^2 = 1cm^2$

$1000mm^3 = 1cm^3$

You may also have to work with a unit of area called **hectares**.

1 hectare (ha) = $10000m^2$

What is $85000m^2$ in hectares?