When measuring the length, area, or volume of an object, we want to choose the most appropriate unit. Sometimes the units we are given are not the easiest to deal with, they may be too large or too small and make calculations cumbersome.
A blue whale is 31\,456 \text{ mm} long, a one dollar coin has an area of 0.000\,491 square metres, and an apple has a volume of 0.000\,24 cubic metres. These are all correct measurements, but are they useful? Can you visualise these sizes in your mind?
Now, what if you were told a blue whale is about 32 \text{ m} long, a one dollar coin has an area of 491 \text{ mm}^2, which is a little bit less than 5 square centimetres, or that an apple has a volume of 240 cubic centimetres. These numbers are much more sensible, can make it much easier to visualise and also to make comparisons to other sizes. Sometimes, as in the case of the coin, two different units might both be considered appropriate.
Much like we can express the same length in different units, we can convert from one unit of area to another, and similarly from one unit of volume to another we will make use of the following relationships. Let's first remind ourselves of the length conversions, as we will use these to work out the conversions for area and volume.
Here are some of the length conversions:
\begin{array}{c} 1 \text{ km} &=& 1000 \text{ m} &=& 100\,000 \text{ cm}\\ 1 \text{ m} &=& 100 \text{ cm} &=& 10\,000 \text{ mm} \\ 1 \text{ cm} &=& 10 \text{ mm} &=& 0.01 \text{ m} \end{array}
Convert 6.52\text{ cm} to millimetres.
Length conversions:
\begin{array}{c} 1 \text{ km} &=& 1000 \text{ m} &=& 100\,000 \text{ cm}\\ 1 \text{ m} &=& 100 \text{ cm} &=& 10\,000 \text{ mm} \\ 1 \text{ cm} &=& 10 \text{ mm} &=& 0.01 \text{ m} \end{array}
Here are some of the area conversions:
\begin{aligned} 1 \text{ km}^2 &= 1\, 000\, 000 \text{ m}^2 \\ 1 \text{ m}^2 &= 10\, 000 \text{ cm}^2 \\ 1 \text{ cm}^2 &= 100 \text{ mm}^2 \end{aligned}
Here are some of the volume conversions:
\begin{aligned} 1 \text{ m}^3 &= 1\, 000\, 000 \text{ cm}^3 \\ 1 \text{ cm}^3 &= 1000 \text{ mm}^3 \end{aligned}
Convert 6 \text{ km}^2 into \text{m}^2.
The rectangle below has side lengths given in centimetres.
Convert the dimensions of the rectangle into metres.
Find the area of the rectangle in square metres.
Convert 9.77 \text{ cm}^3 into \text{mm}^3.
Area conversions:
\begin{aligned} 1 \text{ km}^2 &= 1\, 000\, 000 \text{ m}^2 \\ 1 \text{ m}^2 &= 10\, 000 \text{ cm}^2 \\ 1 \text{ cm}^2 &= 100 \text{ mm}^2 \end{aligned}
Volume conversions:
\begin{aligned} 1 \text{ m}^3 &= 1\, 000\, 000 \text{ cm}^3 \\ 1 \text{ cm}^3 &= 1000 \text{ mm}^3 \end{aligned}
So far we have looked at units of volume and area that are based of our metric units of length, millimetres, centimetres, metres and kilometres.
But there is one special unit of area that does not quite fit the pattern of the others. It is a very useful measurement that helps fill the gap between a square metre (roughly the size of a desk) and a square kilometre (the size of several city blocks).
That's where the hectare comes in.
Here is the hectare conversion:
1 \text{ hectare}= 100 \text{ metres} \times 100 \text{ metres}= 10\,000 \text{ square metres}
Hectares are useful for describing area for things like sporting grounds, farms and parks. To be able to remember the size of a hectare, it helps to see how it is derived, and how it compares to the square metre and square kilometre.
Express 54\,800\text{ m}^2 in hectares.
Hectare conversion:
1 \text{ hectare}= 100 \text{ metres} \times 100 \text{ metres}= 10\,000 \text{ square metres}
A hectare is a unit used to describe area of any shape with 1 \text{ hectare}= 10\,000 \text{ m}^2.