What is the relationship between the units of measurement for the volume of liquid and of a solid object?

Answer 1

Not being sure of what you have in mind by 'relationship', let's assume you are referring to the mundane practice of measuring everyday Newtonian objects, not celestial objects or atomic or subatomic particles, nor are venturing into emotional or metaphysical realms.

Perhaps the relationship comes simply from how you make the measurement. If you want to measure the volume directly by, say, laying a tape measure along the length, height and depth of a cube, obviously the cube has to be solid. On the other hand, the volume of a liquid is usually measured in a calibrated container such as a measuring cup.

To get the volume of an irregular solid object, such as a rock, one can measure the volume of enough water in a calibrated container to cover the rock, add the rock, and remeasure. The difference between the volumes with and without the rock is the volume of the rock. (This method is used to measure a volume of solid fat in baking. Say you want a half cup of fat, so you add just enough fat to half a cup of water to bring the water level to the one cup mark.)

You may have noticed that measuring cups used in kitchens in the US are often calibrated in ounces (oz). And ounces measure weight not volume, right? So what's going on here?

I think the answer lies in the observation that 1 milliliter (ml) of distilled water at 4 degrees Celsius at sea level always weighs 1 gram (g). Furthermore 1000 ml of such water is defined as 1 liter (L), 1 cubic centimeter (cc) as 1 ml, and 1 fluid ounce equals 29.6 ml.

So, if you wanted your volumes in, say, cc's you would multiply the volume in fluid ounces by 29.6 cc/ozzperiodz

Laboratory scientists, even in America, prefer using the metric system because conversions are all based on multiples of 10 so are less cumbersome.

Or if you knew the density of the solid and the liquid, you could weigh each of them and convert to volumes, i.e. weight in pounds (lbs) divided by density in lbs/cubic inches would give you volume in cubic inches. Did you notice that you can get the density of the rock whose volume you measured above by weighing it?

So relationships are also involved in conversions between units of measurements.

For example in the metric system: The volume of a solid object, say a cube, could be measured in units of length such as meter (m).

The volume of a cube that is 1 m long by 1 m high by 1 m deep equals 1 cubic m.

One cubic m of liquid equals 1,000 liters (L). These volumes are exactly the same even though they are expressed in different units, and their measurements may have been obtained in different ways.

There are 100 centimeters (cm) in a meter, so on a smaller scale, 1 cubic centimeter (cc) is a milliliter (ml). Liquid volumes may be expressed in ml or cc

Since 1 liter is 1000 ml, and 1 kilogram is 1000 grams, therefore 1 liter (L) weighs 1 kilogram (kg).

The calculation is:

(1 g/1 ml) x (1000 ml/L) x (1 kg/1000 g) =

rearrange to: (1/1) x (1000/1000) x (ml/ml) x (g/g) x (kg/L) =

1 x 1 x 1 x 1 x kg/L = 1 kg/1 L

(Of course if you're writing this on a piece of paper by hand, you omit rearranging and simply cross off units or numbers that are identical in both the numerator and the denominator, and collect what's left for the result.)

The example above is a short and simple equation, one you may be able to do in your head. The number of factors in such equations depends on where you're starting, where you want to end up and what equivalencies you need to employ. You may, on occasion, have an equation with many more equivalencies in both metric and English/American units. Writing them down, being careful to include ALL the measurement units and getting them in the appropriate position as numerator or denominator as you develop the conversion equation will keep you on track even if there are too many equivalencies to manipulate in your head.

Dictionaries have whole tables of measures, as do various handbooks.

This technique is called factor analysis, if I remember correctly, from my high school drafting class taught by Albert Phinney. It is one of the most useful things I learned in any of my many years in school.

ummm.... not so sure about his answer probably right but if ur still in school like 5-11 grade the relation might be that both have mass which makes them matter and take up space. One is measured by LxWxH while water must be put into a graduated cylinder.

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Reply from NigelG (as I left the first answer intact but the site blames the subsequent respondent for the lot):

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To answer the original question, assuming it's about SI units, and using the proper French spellings:

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The Relationship between the Units of Volume of a Liquid and a Solid in the Metric system is simply that you can use the Cubic Metres (or appropriate multiple / division) for fluids or solids, or the Litre for fluids only.

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( 1 litre = 1000 c.c.; 1000 litres = 1 cubic metre and only if its pure water, has a mass of 1Tonne)

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That is all that the question asked! And 'LxWxH'...works ONLY for the regular cuboid!!!

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I have had to become familiar with using both systems professionally and in daily life and hobbies over some 40+ years, so I can assure you that you DO NOT NEED 'Dimensional Analysis' , Algebra and bizarre chain-conversions I have seen in many "Answers" answers calculated to baffle further, the hapless questioner. I even saw one so tangled it somehow made "...100 000cm = 4km"!

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Clearly you must ensure continuity, such as area-must-be-to-area, but otherwise need ONLY to know where to look up the appropriate multiplier to convert any quantity of any particular one unit in one system to its equivalent in the other: [Imp. Unit X multiplier = SI Unit]