LENGTH
How far is it to Detroit?
How long is your nose?

You would answer these questions with lengths.  A length is a distance from one place to another.  Sometimes you get lengths for odd-shaped objects, like when you get fitted for clothes... your waist is not a straight line, so it gets measured with a flexible tape or string.
The point is that length has only one dimension.  


AREA
How much floor space is in this room?
How big is that wall?

You would answer these questions with areas.  Areas depend on length and width, so are said to be two dimensional.  For rectangular surfaces, all you have to do is multiply the lengths of the two sides together.  If you were to measure the two lengths in meters, then your answer for area would be in square meters (m2).  When people buy houses, they are told the floor space in square feet.


VOLUME
How much space is in your refrigerator?
How big are you?

These questions are answered with volumes.  Volume is three dimensional.  For a box shaped object, all you do is multiply length * width * height.  Multiplying like this gives you an answer in cubic meters (m3).  When you buy a fridge and want to know how much stuff you can put inside, you look at tthe tag and it will say something like "capacity = 21 cubic ft".



Let's apply what we've learned...  Let's say that the big cube above measures 3m on each side.  This means that each little cube making up the big cube is one meter on all sides, right?
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