How do conversions involving volumes (ft3 to m3) differ from standard conversions (ft to m)?
Answer:
The only difference is the cube. Ill give you an example:
1ft = 0.3 meters. Therefore if you have lets say 2.3 ft and you want to convert it to meters then use dimentional analysis
2.3 feet x 0.3 meters=0.7meters
.....1 foot
Now lets say you want to convert ft3 to m3 you would do it the same way but you cube the conversion. Ill show you
8.2ft3 x (0.3mx0.3mx0.3m)>> 8.2ft3 x 0.027m3=0.22m3
.......1ft x 1ft x 1ft.......1ft3
The conversion factors for volume (m^3) are the cube of the conversion factors for linear measure (m). Using metric so we don't have to contend with long decimals,
1 m = 100 cm
1 = 100 cm/1 m = 1 m/ 100 cm
cubing,
(1 m)^3 = (100 cm)^3
1 = (100 cm)^3/(1 m)^3 = (1 m)^3/(100 cm)^3
Using unit fractions like those above, dimensions can be cancelled like variables.
It's not chemistry, just math. The ratio of cubic volumes is the cube of the linear relationships. As a simple example let's skip the metric conversion and compare a cubic foot to a cubic yard. The cubic yard is three feet on each side so it is 3x3x3 = 27 cubic feet. Just imagine a Rubic's cube where each of the little cubes is a foot across - there are 27 of them (counting the pivot in the middle) making up the larger cube.
Similarly a foot is 0.3048 metres, so a cubic foot is that number multiplied by itself three times, or about 0.028 cubic metres. Invert that number and you find that a cubic metre is about 35 cubic feet.
Incidentally, the inch is defined as 2.54 centimetres, so you can do these conversions to whatever level of precision you like.
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