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# Conversion of ice to water

How much water is in an 8 ounce cup of ice chips that are 1/2 an inch wide, 1/2 an inch long, and 1/5 an inch thick?    Show how you came up with the solution.

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OrdinaryGeek
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1 Solution

Commented:
The question is not clear.
Does the ice weigh 8 ounces? Does the ice exactly pack an 8 fluid ounce cup?

The density of ice is 0.92 that of water. So if know the volume of ice you can calculate the volume of water by multiplying by 0.92.

The (imperial) density of water  62.416 pounds per cubic foot at 32°F (though you should really be using SI metric units).

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Commented:
PS: A cubic foot is 1728 cubic inches
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Author Commented:
I have an 8 fluid ounce measuring cup filled up with ice chips.
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Author Commented:
Btw, I figured you needed the size of the ice chips to get a precise measurement.  Larger ice cubes would have more space between them.
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Commented:
Is this a homework question?
Or a puzzle?
Or an exercise in estimation?

Can you pour the ice into a measuring cup and put it in a microwave?
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Commented:
Can you weight the cup?  Or count the chips?
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Commented:
If it is a square or rectangular cup then you might be able to fit the cubes with no space between them. You really need to know the shape and dimensions of the cup. If it's a cylinder the diameter and height.
How many ice cube you get in will also depend on how they are stacked.
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Author Commented:
LOL No, it's not a homework question.  I'm done with school (and obviously math wasn't my major).   I guess it is more of a puzzle.  I was just sitting at work and had a curiosity as to how much water I am consuming when I eat a cup of ice chips.

Actually, that was my first idea - to nuke the cup and see the quantity, but that would make it too easy on you wouldn't it?

Since it most likely is going to be an estimation on the amount of water, just use the typical 8 ounce coffee cup measurements (one that is round/cylindrical, never seen a square coffee mug).

I thought this was the math/science question area - no bored mathmaticians here that want to take a shot at this?
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Commented:
If by an 8 oz cup you mean one that will hold 8 oz of water and you fill it with ice leaving a negligible amount of air, you will have about 8 times 0.92 ounces of water. (0.92 is the density of ice.).
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Commented:
Assuming no air in the ice, between
0.0000007513 and
0.0002163878 liters,
depending on how many ice chips with those dimensions you can fit in the 8 oz cup, which depends on the shape of the cup and how the chips are packed.
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Author Commented:
Ozo, how did you get those numbers?   I want to know how many ounces of water I will get.
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Commented:
1 US fluid ounce = 0.0296 litres
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Commented:
0.0296 liters/fl oz * 8 fl oz * 0.92 liters of water/liter of ice * x, where x is the packing density of the ice chips.

That works out to 0.218*x liters per cup.  Guess 80% packing density on the ice chips, that makes about 170ml per cup.

Chew that much ice often, and you'll hurt your teeth.
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Author Commented:
lol  Thanks Nova.  Since you were the only one that gave me an approximated answer (that made sense after I converted it to US ounces), I'm giving you the points.

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Commented:
If you want the answer in ounces, just leave off the 0.0296 factor at the beginning.

7.36*x fl oz.  If x=80%, about 6 fl oz.
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Commented:
each 1/2 an inch wide, 1/2 an inch long, and 1/5 an inch thick chip contributes 0.0007513 liters of water
at most 288 such chips can fit in 8 fl oz
but there is no way to determine from the information given how many such chips you can actually fit in your cup
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