Convert between different units of area and volume
First, you need to know your basic units and how they relate to each other.
Lengths
1km = 1000m
1m = 100cm
1cm = 10mm
Weights
1tonne = 1000kg
1kg = 1000g
1g = 1000mg
Capacity
1L = 1000cc
1L = 100cl
1cl = 10ml
1ml = 1cc
When you convert from a larger unit to a smaller unit you multiply
(for example, for every 1m you have 100cm, so you need to multiply by 100 to get metres in centimetres)
When you convert from a smaller unit to a larger unit you divide
(for example, for every 1000g you have 1kg, you have to divide by 1000 to get grams in kilograms)
How to convert between units of areas
It is important to remember that areas are not units of 'cm' but 'cm^{2}', it is no longer a length.
1m^{2} means a 1m by 1m square. This means a 100cm by 100cm square. So the area of this square in cm is 100cm x 100cm = 10,000cm^{2}
For example
What is 5cm^{2} in mm^{2}?
5cm^{2} is the same as 5 lots of 1cm^{2} squares (It is NOT a square that 5cm by 5cm, as that would give you a 25cm^{2} area!)
A 1cm^{2} area is given by a 1cm by 1cm square. So 1cm^{2} is a 1cm x 1cm square. This is the same as a 10mm x 10mm square. So the area of one such square, in millimeters squared, is 100mm^{2}. Hence 5cm^{2} = 500mm^{2}.
How to convert between units of volume
We use the same method for converting between units of areas to converting between units of volume.
Volumes are in cm^{3}, it has 3 dimensions!
A 10mm^{3} is cube with all sides 10mm (10mm x 10mm x 10mm). This means a cube with all sides 1cm (1cm x 1cm x 1cm). The volume of this cube is 1cm^{3}_{.}
For example
What is 3cm^{3} in m^{3}?
A solid that has a volume of 3cm^{3}, has the same volume as 3 cubes that have volumes of 1cm^{3}.
A 1cm^{3} is a cube with all 3 sides of 1cm. This is the same as a cube with all 3 sides 0.01m. So the volume of one such cube, in metres cubed, is 0.01m x 0.01m x 0.01m = 0.00001m^{3}. Hence 3cm^{3 }= 0.00003m^{3}.
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