In a dimensional analysis problem they take 6.20L x (1ft^3/28.3L) x (12in^3/1ft^3) to get 378 in^3. Why do they express the 12in^3 as 12x12x12? To me it would be expressed as 6.20/28.3*12 to get 2.6289.... ? I may be missing an easy concept here?

In addition, This relates to volume in chemistry as is why I am asking this; How does one understand or express cubic units? For example, is 12cm^3 essentially 12x12x12? But.. A rectangle could be 3x4x1 which is 12cu. But then what is confusing do you then take the 12x12x12?

  • $\begingroup$ The source of your confusion would be eliminated if you format your braces properly. 12cm^3=12cm*cm*cm. But, (12cm)^3=12*12*12 cm*cm*cm. $\endgroup$ – Gaurang Tandon Apr 2 '18 at 10:27
  • $\begingroup$ @GaurangTandon So 12 cubic centimeters is simply 12cm*12cm*12cm? $\endgroup$ – user62216 Apr 2 '18 at 17:55
  • $\begingroup$ 12 cubic centimetres is not that. Take a cube of side 1cm*1cm*1cm, that's one cubic centimetre. Multiply it by 12, that's 12 cubic centimeters. $\endgroup$ – Gaurang Tandon Apr 3 '18 at 0:59

12 cubic metre means $$\pu{12 \times 1 m \times 1 m \times 1 m}$$So if you wish to convert it into centimetres, it becomes $$\pu{12 \times 100 cm \times 100 cm \times 100 cm}$$ as $\pu{1 m = 100 cm}$

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  • $\begingroup$ So what would 12 cubic centimeters be ? 12x1cmx1cmx1cm? $\endgroup$ – user62216 Apr 2 '18 at 4:07
  • $\begingroup$ Yeah $\mathstrut$ $\endgroup$ – Ivan Neretin Apr 2 '18 at 4:35
  • $\begingroup$ How would this be represented by a shape? Is the shape irrelevant here? $\endgroup$ – user62216 Apr 2 '18 at 5:26

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