Volumes of Fluids

Say you pick up a two litre container of milk from the shops.  It’s full of milk, which is a liquid or fluid.  How much volume does the container take up?  Well, the volumes of fluids are measured using a special set of units, called fluid units.  For example, the volume of the container of milk is 2 litres – ‘litres’ is one type of fluid unit.

These fluid units can easily be converted into the normal volume units of cubic centimetres, metres etc…

First up we’ve got millilitres -  this is the sort of fluid unit that you’d use to measure out a dose of medicine or a small amount of liquid in a food recipe.  One millilitre is the same volume as one cubic centimetre.  The symbol for millilitres is ‘mL’ or ‘ml’.  Some people use a capital ‘L’, some people use a small ‘l’.  Find out which your teacher prefers!

Then we’ve got litres, which is what you’d use to measure how big a container of milk is, or how many litres of petrol you could put in a car.  There is no common normal volume unit for a litre.  However, there are 1000 cubic centimetres in a litre, and there are 1000 litres in a cubic metre.  The symbol for litres is ‘L’.  Some people will use little ‘l’ instead.

Last up we’ve got kilolitres, with the ‘kilo’ meaning ‘thousand’.  So a kilolitre is just 1000 litres.  This means that a kilolitre is the same volume as 1 cubic metre.  The symbol for kilolitre is ‘kL’ or ‘kl’.

Here’s a summary of these main fluid units:

 Name Symbol Same as Millilitre mL 1 cm3 Litre L 1000 cm3 or 0.001 m3 Kilolitre kL 1 m3

Sometimes fluid units are used to describe something which isn’t a fluid.  For instance, eskies for putting drinks in are usually described by their volume, but using fluid units.  An esky might be described as being a ‘120 Litre’ esky.  If you buy a large backpack for hiking, it’s also usually described in terms of fluid units – a large backpack for an adult might have a 90 litre capacity.

How big a cubic metre really is

People often buy earth or mulch for their gardens to put down on flowerbeds.  Usually this involves having to wheelbarrow the stuff around to various points in the garden and then spreading it out on the ground.  For a typical backyard garden someone might buy say 2 cubic metres of earth to do up some new garden beds.  This gets delivered by truck to their house and dumped in a pile, but then they’ve got to spread it around.

A typical large wheelbarrow might have a capacity of 50 litres.   How many trips are you gonna have to make to spread out 2 cubic metres of earth?

Well, 1 cubic metre is the same as 1 kilolitre, which is 1000 litres.  We’ve got 2 cubic metres, so we’ve got 2000 litres of earth.  So if we do a full wheelbarrow load each time:

40 full loads is a lot of trips with the wheelbarrow –gives you an idea how big cubic metres really are!

A typical adult human body has a volume of somewhere between 60 and 90 litres.  This means our volume is only a little bigger than a wheelbarrow!  So if you had a cubic box which was 1 metre by 1 metre by 1 metre – you could cram over 11 humans into it!  Of course it wouldn’t be very comfortable…

 What is the volume in kilolitres of a swimming pool which is just a rectangular prism 10 metres by 5 metres by 1.5 metres deep everywhere? Solution Well, this swimming pool doesn’t have a sloping bottom from shallow to deep end – everywhere is the same depth.  So we just have to multiply the three side lengths together to get the volume in cubic metres:                                                       Now we know that one cubic metre is the same as 1 kilolitre.  So the answer is just 75 kilolitres.