Volume and capacity. Technically, there is

a difference. Volume is the amount of space occupied by an object, and capacity is the

amount of space inside an object. We tend to measure volume in cubic metres, cubic centimetres,

and so on, and capacity in litres, millilitres, kilolitres. However they are somewhat interchangeable. To convert between volumetric units, I use

an extension of the trick I showed you for area. Instead of drawing a square, draw and

label a cube. So, for cubic millimetres into cubic centimetres, label each dimension of

the cube with one centimetre. Then the volume will be one cubic centimetre. But each one

centimetre side is ten millimetres. So the volume is also ten by ten by ten, which is

one thousand cubic millimetres. Similarly, for the next pair, label the sides

with one metre, for a volume of one cubic metre. And each metre is one hundred centimetres,

so the volume is also one hundred times one hundred times one hundred, which is one million

cubic centimetres. And you could do the same for cubic kilometres,

but to be honest, I don’t actually know of anything that’s measured in cubic kilometres.

The unit is just too big. However large volumes are often measured in

megalitres and gigalitres, dam capacity for example. How do we convert between cubic metres

and litres? Unfortunately there’s no easy trick to remind

you. You just need to remember. One cubic centimetre is the same as one millilitre.

Or, one cubic metre is the same as one kilolitre, one thousand litres. Pick one of these comparisons,

and remember it. Then you can easily convert between the other

capacity units. It’s just like it was for length, with the standard SI prefixes. Note

that the SI abbreviation for litres is a capital L. Let’s try a few. Fifty-two cubic centimetres

is how many cubic millimetres? The new unit is smaller, so I need more: multiply. Fifty-two

times one thousand is fifty-two thousand cubic millimetres. Three point six cubic metres is how many cubic

centimetres, and how many litres? Cubic centimetres first. They’re smaller than cubic metres,

so I need more: multiply. Three point six times one million is three million six hundred

thousand cubic centimetres. And litres? You can go either from the cubic metres to kilolitres,

or the cubic centimetres to millilitres. In general it’s better to go from information

given to you rather than something you’ve calculated yourself, so let’s go from cubic

metres to kilolitres. It’s three point six kilolitres, which is three thousand six hundred

litres. Seventeen litres in cubic centimetres? Well,

a cubic centimetre is the same as a millilitre. Seventeen litres is seventeen thousand millilitres,

so that’s seventeen thousand cubic centimetres. And finally, one hundred and sixty megalitres

into cubic metres. Well, a cubic metre is the same as a kilolitre. One hundred and sixty

megalitres is one hundred and sixty thousand kilolitres, so that’s the same as one hundred

and sixty thousand cubic metres. One final note about unit conversions. When

you’re problem solving, always convert units first, right away. It’s almost always easier

to do it at the start than to convert your calculated answer at the end.