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Math and Arithmetic

How are volume units related to length?


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September 01, 2013 6:43PM

Here's all you need to know to convert between volumes (i.e. m^3 to cm^3).

Volume is distance x distance x distance. Any formula you think about. Cube=L^3 or LxWxH, sphere is 4/3 pi x r^3 (r is distance), cylinder = pi x r^2 x L (r x 2 and L).

Why is this? because volume extends to the 3rd dimension.

What used confuse me was when my maths teacher said that there were 1,000,000 cm^3 in a metre cubed. I knew that 100cm were in a metre but it confused me passed this. Thing is, that difference becomes cubed due to it being 3rd dimension. i.e. the difference is actually 100x100x100, i.e. 1 million.

Some other things to remember. 1 cm^3 is the same as 1 millilitre. cc actually means centimetre cubed, i.e. cm^3. As milli means 1 thousandth there are 1000ml in a litre, therefore 1000cm^3 in a litre.

By definition, 1 cubic centimeter (cc or cm3) = 1 milliliter = 1 mL = 1/1000 L. ("Milli" means 1/1000th.) In this way, a standard unit of length, the meter, is directly related to a standard unit of volume, the litre.

Thus, there are 1000 mL in a Litre, and that means that one cubic meter = 1000 L x 1000 mL/L = 1,000,000 mL = 1,000,000 cc (or exactly 1x106 cc), NOT 1000 cc as the previous contributor stated.

When the previous contributor wrote about a cube, he should have been more clear and wrote: "In the special case of a cube, volume = (length of any side of the cube)3 since all sides of a cube are of equal length."

In my opinion, the remainder of what the previous contributor wrote is correct and is a good description.

If you are asking about the standard units of measure used, 1 liter is exactly 1000 cubic centimeters, and one US liquid gallon is exactly 231 cubic inches.

If you are asking about calculating volume, that can be determined from length measurements.

In the special case of a cube, volume = length3.


In all other regular objects with straight sides (prism, pyramid, etc.) the volume will have a relationship to the length of any particular object that depends upon the geometry of the shape. In a rectangular prism, such as a shoe box, the volume is directly proportional to the length of any single dimension.


For spherical shapes, the volume is 4/3 pi r3, where r is the length of the radius.

For other shapes, the volume formula may be more complicated, and for irregular shapes, the volume may have to be estimated.


Some irregular shapes' volumes cannot be estimated or measured by length. The volume of a daisy flower, for example, can not readily be measured by conventional length measurements because the shape of the object (all those petals, stamen, stigma, filaments, and sepals, not to mention the stem, leaves, and roots) make it too difficult to calculate the volume by measure straight lengths. Other methods are required to measure the volumes of such irregular objects, including liquid displacement or three dimensional surface scanning or tomography.