[bonanova]

Al Gore is stranded on a cubic iceberg that measures 100 miles on a side.

To pass the time until his rescue, he recites from memory all his speeches on Global Warming.

The hot air he produces melts the iceberg.

What is the resulting rise in sea level world wide?

You may assume:

1. Water expands 10% when it freezes.
2. The earth has a 4000 mile radius.
3. Three quarters of the earth's surface is covered by connected oceans.

[Guest]

201057280 sp miles of Earth * 3/4 water surface area = 150792960 sq miles

1 Mil cubic miles / 1.1 (ice/water ratio) = 909090.9091 cubic miles

909090.9091 miles³ / 150792960 miles² = 0.006028735 miles or 31.831725 feet

[Guest]

and if it the side was horizontal - sheet ice? would it make a difference?

It's 100mi. cubed all sides are 100mi....

I don't get how people are saying the level will not rise when there is no way 90% of the icecube could be under water..that would mean it is sitting in a 100sq.mi. piece of ocean that is 90 miles deep...also for those that did get an answer, how did you arrive at it when you don't know where the icecube is? It could be displacing 2 miles of ocean or 7 miles of ocean depth..or what if it's sitting in only 1,000 feet of water? Or are you just figuring what the icecube would add to the current level, as if it were melted and poured into the ocean?..just off the top of my head, I'd think it would only rise a matter of inches, or cms...I don't know tho

[Guest]

Would just like to point out that whilst the initial rise in sea level will not be much, the heat energy from sun in form of light will now be absorbed by the extra water, instead of mostly reflected off ice. This will increase overall ocean temperatures and further accelerates the melting of other icebergs.

[bonanova]

It's 100mi. cubed all sides are 100mi....

I don't get how people are saying the level will not rise when there is no way 90% of the icecube could be under water..that would mean it is sitting in a 100sq.mi. piece of ocean that is 90 miles deep...also for those that did get an answer, how did you arrive at it when you don't know where the icecube is? It could be displacing 2 miles of ocean or 7 miles of ocean depth..or what if it's sitting in only 1,000 feet of water? Or are you just figuring what the icecube would add to the current level, as if it were melted and poured into the ocean?..just off the top of my head, I'd think it would only rise a matter of inches, or cms...I don't know tho

Point taken.

I'm not sure what normal practice dictates when knowledge outside the OP comes to bear on a solution.

My approach [while others may differ] is to assume nothing of consequence outside the OP, and see if a solution can be obtained.

Good example here is Hole in a Sphere.

My intent was to imply a mathematical earth [as described] having oceans of sufficient depth to float the cube.

I could have avoided the issue by making the cube edges 100 feet, and that might have been the better thing to do.

But some might then answer: "by an insignificant amount" where what I was looking for was "not at all."

[Guest]

Point taken.

I'm not sure what normal practice dictates when knowledge outside the OP comes to bear on a solution.

My approach [while others may differ] is to assume nothing of consequence outside the OP, and see if a solution can be obtained.

Good example here is Hole in a Sphere.

My intent was to imply a mathematical earth [as described] having oceans of sufficient depth to float the cube.

I could have avoided the issue by making the cube edges 100 feet, and that might have been the better thing to do.

But some might then answer: "by an insignificant amount" where what I was looking for was "not at all."

sorry, I did'nt mean to pick apart your puzzle...

My initail thoughts were that there would be 0 rise in level...but then I realized the iceburg would not be able to float in any ocean, and thought maybe you were in fact looking for a number...

It's just that if it seems easy to me, then I'm usually wrong, and if it is a puzzle coming from an author (like yourself) who usually throws complex mathematical problems at us (complex to me anyway), then I'm almost certain I'm wrong...so it made me overthink it and doubt my original thoughts I geuss..

[Guest]

You didn't account for the changing surface area of Earth as it floods

I could do the math but I'm too lazy. Someone on page three has probably already posted the correct answer.

[Guest]

You didn't account for the changing surface area of Earth as it floods

I could do the math but I'm too lazy. Someone on page three has probably already posted the correct answer.

how would the total surface area of the earth change?..the surface area of the ocean would increase, while at the same time, the surface area of the land would decrease..

the answer is 0 rise in sea level...imagine you have a large chunk of ice floating in the Pacific, 1,000mi. long by 1,000mi. wide by 2mi. thick(deep)...our geologist..we'll call him Dr. Bonanova, runs down from his suite on the 50th floor of the Trump Tower..heads on down to the ocean and takes out his "measure all" measuring stick, and records 35 units...overnight Al Gore sneaks onto the iceburg, and holds a global warming conference there, and completly melts the iceburg...now when Dr. Bonanova takes his recordings the next day he'll still record 35 units...because when the initial recordings took place, it already accounted for the displacement of water the iceburg created..ice expands 10% from its water state...ice floats such that 10% is bobbing above the ocean surface...so when it melted it just replaced the area the ice was taking up, by water..meaning no change in sea level...same reason why if the northern ice cap were to melt, there would be such an insignificant rise in sea level(since it is a floating ice sheet), that scientists don't even account for it(when talking about sea level increases)..

[bonanova]

how would the total surface area of the earth change?..

I think this refers to the increase of a sphere's area as its radius increases.

If sea level were to rise, say, by 1 inch, that would add 1 inch to the sea's

spherical radius, and the sea's spherical surface area would increase

accordingly. So if a given increase of sea water produced the first inch

rise of sea level, a slightly larger increase of sea water would be needed

to produce the next 1-inch rise. And so on.

Ah... re-reading, now I think this refers to the increase in sea area, which

began in the OP as 3/4 the area of a 4000-mile-radius sphere, but increases

as land masses are inundated, giving up their area to the sea.

Both apply. But while the first is easier to calculate; the second is probably

a larger effect.

[Guest]

I think this refers to the increase of a sphere's area as its radius increases.

If sea level were to rise, say, by 1 inch, that would add 1 inch to the sea's

spherical radius, and the sea's spherical surface area would increase

accordingly. So if a given increase of sea water produced the first inch

rise of sea level, a slightly larger increase of sea water would be needed

to produce the next 1-inch rise. And so on.

Ah... re-reading, now I think this refers to the increase in sea area, which

began in the OP as 3/4 the area of a 4000-mile-radius sphere, but increases

as land masses are inundated, giving up their area to the sea.

Both apply. But while the first is easier to calculate; the second is probably

a larger effect.

All that should'nt have any bearing on the initial math equation to figure out the rise in sea level..even if more and more land is consumed (increasing ocean area) the overall average sea level will still have increased...since "most" land is above sea level, then that means the sea has risen enough to overcome it, therefore the sea level has raised..the only way I see that it would affect any calculations, is if it reaches land further inland, that is in fact below sea level, then it would act sort of like a dam, and theoretically it would "level" off some sea level rises, and throw off your calculations (probably a very small amount)...basically if you took measurements from anywhere in any ocean, and you know that a significant amount of ice(that was originally on top of land) has melted more than new ice has been brought back..you will have an increase in sea level, no matter how much land is being consumed..

So I would go with whatever mathematical equation works to figure the expected rise..without worrying about the after affect of the differences in area..

[Guest]

Can we assume that 9/10ths of the iceberg is below the water line and 1/10th is above the water line? (Definition of an iceberg.)

Can we assume the water is deep enough to float the iceberg? Otherwise, it would not be an iceberg. It would be a glacier.

The answer is: No change in sea level.

Ice is less dense than water. That is why it floats. The 10% expansion mentioned in the problem is actually a contraction.

A cubic meter of ice weighs 10% less (and is less dense) than a cubic meter of water.

When a cubic meter of ice melts, it becomes 0.90 cubic meters of water.

That 1/10th of the iceberg above water would sink to the water line. The volume (and sea level) would remain the same.

The problem changes if we re-defined sea level to be the top of the iceberg.

Edited July 20, 2009 by Kerrik

[Guest]

Al Gore is stranded on a cubic iceberg that measures 100 miles on a side.

To pass the time until his rescue, he recites from memory all his speeches on Global Warming.

The hot air he produces melts the iceberg.

What is the resulting rise in sea level world wide?

You may assume:

1. Water expands 10% when it freezes.
2. The earth has a 4000 mile radius.
3. Three quarters of the earth's surface is covered by connected oceans.

I dont think there will be any change in the water level. It is obvious from Archimedes principle.

[Guest]

Eureka! - so to speak. The level would rise by the displacement of al gore's weight or not.. (depending on whether measures taken from before AG stood on the ice-cube/berg or after)

[Guest]

Well, we've now had the correct answer posted about a dozen times (assuming we take the definition of 'iceberg' at face value and require the entire mass of the ice to be floating.) ...

Nitpickers take note: (assuming Al Gore's 'hot air' is not the sole source of the latent heat of melting) ... a melting iceberg cools the ocean unless the average water temperature is already 0 degrees Celsius. Heat from the ocean is extracted by each molecule of H2O as it changes phase. Also water is most dense at 4 degrees Celsius. Therefore if the iceberg was floating in water that was warmer than 4 degrees C, there would be a slight *DROP* in sea level due to the contraction of the sea water as it is cooled. If the iceberg was floating in water colder than 4C, there would be a slight sea level rise.

Of course icebergs consist of fresh water and sea water is saline. One might expect some slight effect from the net decrease in salinity of the ocean as the iceberg melts, but in fact there is no effect. Salt water is more dense than fresh water at the same temperature, but there is no change in volume because the sodium and chlorine ions take up no volume by themselves (they "squeeze" snugly in between the liquid water molecules. it's a great experiment to try--as you pour salt into water and dissolve it, its volume does not change at all: it's as if the salt had simply dissapeared. The same experiment done with sugar shows that adding sugar *does* increase the volume of the water because the sugar molecules are too big to squeeze in between the water molecules).

[Guest]

Well, we've now had the correct answer posted about a dozen times (assuming we take the definition of 'iceberg' at face value and require the entire mass of the ice to be floating.) ...

Nitpickers take note: (assuming Al Gore's 'hot air' is not the sole source of the latent heat of melting) ... a melting iceberg cools the ocean unless the average water temperature is already 0 degrees Celsius. Heat from the ocean is extracted by each molecule of H2O as it changes phase. Also water is most dense at 4 degrees Celsius. Therefore if the iceberg was floating in water that was warmer than 4 degrees C, there would be a slight *DROP* in sea level due to the contraction of the sea water as it is cooled. If the iceberg was floating in water colder than 4C, there would be a slight sea level rise.

Of course icebergs consist of fresh water and sea water is saline. One might expect some slight effect from the net decrease in salinity of the ocean as the iceberg melts, but in fact there is no effect. Salt water is more dense than fresh water at the same temperature, but there is no change in volume because the sodium and chlorine ions take up no volume by themselves (they "squeeze" snugly in between the liquid water molecules. it's a great experiment to try--as you pour salt into water and dissolve it, its volume does not change at all: it's as if the salt had simply dissapeared. The same experiment done with sugar shows that adding sugar *does* increase the volume of the water because the sugar molecules are too big to squeeze in between the water molecules).

That is very cool! Thanks for the explanation.

Of course if hot air (from whatever source) were the cause of the melting, the sea level would have to drop as the ice cube evaporated into the atmosphere.

Come to think of it, if we are to believe in global warming, then we must logically believe that the sea levels would drop as more water evaporates into the warmer and warmer atmosphere. Wouldn't we?

[Guest]

That is very cool! Thanks for the explanation.

Of course if hot air (from whatever source) were the cause of the melting, the sea level would have to drop as the ice cube evaporated into the atmosphere.

Come to think of it, if we are to believe in global warming, then we must logically believe that the sea levels would drop as more water evaporates into the warmer and warmer atmosphere. Wouldn't we?

Until that evaporated water starts to fall back as rain. Another effect of global warming is expected to be stronger storms. It *is* true that a warmer atmosphere can hold more water vapor, but even a tropical atmosphere totally saturated with water vapor can hold only the equivalent of a few inches of liquid water at most. Then it has to start falling out as rain.

Then, if you really want to start looking at complicating factors, consider the extra snow that this warmer atmosphere can deposit on Antarctia. It's too cold on Antarctica for any of the snow that falls to melt. So what can happen is that sea level could actually fall as a result of global warming if snow accumulates on Antarctica faster than the flow of all its glaciers can transport that snow back into the sea to become more icebergs. Al Gore better be ready to give a lot more speeches