Thursday, 26 March 2009

How big is a litre?

Now it is time to think in three dimensions and look at volumes. Start with a circle. You know that its area is π times the radius times the radius. It is easier to say π times the radius squared. If you give this circle a height (h) then it looks like a tin can, and its volume is the base times the height which is π x radius squared x height.

Let’s use this idea of volume to think about litres of water in a water tank. Start by thinking about a metre or 100 centimetres. Have you got an idea of this length? Then think about a square one metre times one metre. This has 10,000 square centimetres in it. Now think of volume by making this square one metre high, so you have one cubic metre. This has 10,000 x 100 cubic centimetres in it i.e. 1,000,000 cubic centimetres.

A cubic metre has 1,000 litres in it. So one litre is 1,000 cubic centimetres which happens to be the size of 10cm x 10cm x 10cm = 1000 cubic centimetres. Check your measuring jug. OK it isn’t a cube but you know it is the same size as a cube with 10cm sides.

That sums it up

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