Eiffel Towers volume
Who knows what is the Eiffel Towers volume? When it's standing and when it's smelted.
Maybe to figure out the volume of it when it's standing is by using pyramid formula? When it's smelted I've though of taking the weight of different tower ingredients and see how much volume each ingredient uses, and that way see how much volume in all.
What I need is for someone give their ideas of how to calculate the volume of the Eiffel Tower. Both when it's standing and when it's smelted. Would appreciate the answer or just a hint.
Maybe to figure out the volume of it when it's standing is by using pyramid formula? When it's smelted I've though of taking the weight of different tower ingredients and see how much volume each ingredient uses, and that way see how much volume in all.
What I need is for someone give their ideas of how to calculate the volume of the Eiffel Tower. Both when it's standing and when it's smelted. Would appreciate the answer or just a hint.
SOLUTION
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ASKER
I've saw that. But it has nothing to do with volume, they take weight and make it 7,000,000 times smaller.
I've googled all kinds of possibility but there are really no answers on the web. That's why I've posted the question here.
I've googled all kinds of possibility but there are really no answers on the web. That's why I've posted the question here.
Well ..
If you go to the wiki:
http://en.wikipedia.org/wi
Look at the last paragraph in that section and key on the references:
http://en.wikipedia.org/wi
and
http://www.vaeng.com/news/
Hope that helps.
If you go to the wiki:
http://en.wikipedia.org/wi
Look at the last paragraph in that section and key on the references:
http://en.wikipedia.org/wi
and
http://www.vaeng.com/news/
Hope that helps.
ASKER
The second link more useful as there are some statistic that maybe be used in calculation. But without formula they're useless...
Still working:
We may have to pay to get the equation, but here are some abstracts that explain it:
http://www.newswise.com/ar
http://74.125.127.132/tran
The last one is a translation. We may need to use the new search engine by wolfram:
http://www23.wolframalpha.
We may have to pay to get the equation, but here are some abstracts that explain it:
http://www.newswise.com/ar
http://74.125.127.132/tran
The last one is a translation. We may need to use the new search engine by wolfram:
http://www23.wolframalpha.
Hot Dog!!!
I think I found it. And in english. Get it at this link:
http://www.exa.unicen.edu.
check it out.
I think I found it. And in english. Get it at this link:
http://www.exa.unicen.edu.
check it out.
ASKER
It's about wind force and all kind of ununderstandable stuff for non professional scientists. What I need is volume.
You are right. The article discusses the shape of the eiffel tower. Apparantly this has been a discussion that has been going on for a long time.
I remember, from a longggggg time ago, working out the volume of a shape that has a singularity in it like the eiffel tower does right at the top. It looks like Weidman took a different approach in coming up with the equation he did, that describes the shape of the tower. And then from the shape of the tower, using differential calculus, you can calculate the volume. I'm just rusty on my differential calculus.
Here's another link where they are talking about a bet, might be the same one your in, and they make some close calculations of the volume:
http://www2b.abc.net.au/sc
Check this one out and I'll keep an eye out for the exact volume using weidman's shape.
I remember, from a longggggg time ago, working out the volume of a shape that has a singularity in it like the eiffel tower does right at the top. It looks like Weidman took a different approach in coming up with the equation he did, that describes the shape of the tower. And then from the shape of the tower, using differential calculus, you can calculate the volume. I'm just rusty on my differential calculus.
Here's another link where they are talking about a bet, might be the same one your in, and they make some close calculations of the volume:
http://www2b.abc.net.au/sc
Check this one out and I'll keep an eye out for the exact volume using weidman's shape.
Maybe to figure out the volume of it when it's standing is by using pyramid formula? When it's smelted I've though of taking the weight of different tower ingredients and see how much volume each ingredient uses, and that way see how much volume in all.
Much depends on what you define as the volume
You have suggested the two most useful methods. Depending on the accuracy you want, it will be easy to do the first method.
If you want an esoteric method you can calculate the volume occupied by the individual atomic particles making up the tower. You will come up with a very small number because most of the volume of a molecule is empty space.
Much depends on what you define as the volume
You have suggested the two most useful methods. Depending on the accuracy you want, it will be easy to do the first method.
If you want an esoteric method you can calculate the volume occupied by the individual atomic particles making up the tower. You will come up with a very small number because most of the volume of a molecule is empty space.
So, do you agree with the measurements arrived at in that last link?
ASKER
Not completely, I'm calculating the volume (m3) not the weight of the volume. Like if you would take a piece of cloth and put it around the tower, and then pure the water inside. I need to know how much water is needed to fill the whole tower.
OK first stupid question - is there a difference between the volume of the tower as it stands and once smelted?
Isn't there a law of conservation of mass? Or are you including the air within the structure?
The weight of cast iron in the tower is generally quoted at 7300 Tons (US) i.e 1.46 million pounds or 662245kg
The density of cast iron is between 6800-7800 kg/m^3 from which you can derive the volume of the puddle of molten iron.
However the total weight of the tower (excluding air) is about 10000 tons (US) so you'll need to factor in the 2700 tons (US) of other materials.
If you want a quick approximation for volume place a close fitting cylinder around it (see the link above)
if you divide the cylinder into 4 quadrants lengthwise then each quarter contains roughly one half tower (and internal air) and one half external air so half the volume of the cylinder is tower with its air within.
Isn't there a law of conservation of mass? Or are you including the air within the structure?
The weight of cast iron in the tower is generally quoted at 7300 Tons (US) i.e 1.46 million pounds or 662245kg
The density of cast iron is between 6800-7800 kg/m^3 from which you can derive the volume of the puddle of molten iron.
However the total weight of the tower (excluding air) is about 10000 tons (US) so you'll need to factor in the 2700 tons (US) of other materials.
If you want a quick approximation for volume place a close fitting cylinder around it (see the link above)
if you divide the cylinder into 4 quadrants lengthwise then each quarter contains roughly one half tower (and internal air) and one half external air so half the volume of the cylinder is tower with its air within.
ASKER
Standing, I mean how much water is needed to fill the tower. (if close all the gaps)
Smelted, mean like if you smelt down the tower and put it inside of a container. (so only the metal and other ingredients of the tower without the air)
Smelted, mean like if you smelt down the tower and put it inside of a container. (so only the metal and other ingredients of the tower without the air)
ASKER
Well, I've already went my own way and divided the tower in 3 cut pyramids, and used a formula for that. And I've got 841 060 m3
But still don't have any idea of a smelted one.
But still don't have any idea of a smelted one.
So...
Let's make our own rough calculation by using the volume of a pyramid. That volume is:
area of base * height * 1/3
base is 125 m each side
height is 312.27m
So 125 * 125 * 312.27 * .333333 = 1626406.087359375
or 1,626,406.16 m^3
one million six hundred twenty six thousand four hundred six qubic meters.
Does every on agree that is close.
Let's make our own rough calculation by using the volume of a pyramid. That volume is:
area of base * height * 1/3
base is 125 m each side
height is 312.27m
So 125 * 125 * 312.27 * .333333 = 1626406.087359375
or 1,626,406.16 m^3
one million six hundred twenty six thousand four hundred six qubic meters.
Does every on agree that is close.
ASKER
Pyramid formula won't work it's nearly double as much.
To get as close as possible is to divide the tower in 3 cut pyramids.
Formula for cut pyramid is:
V = 1/3 × h × (G + ^G × ^g + g)
And i get 8,5 tons which is very close.
Now need to know how much will fill the tower when it's smelted.
To get as close as possible is to divide the tower in 3 cut pyramids.
Formula for cut pyramid is:
V = 1/3 × h × (G + ^G × ^g + g)
And i get 8,5 tons which is very close.
Now need to know how much will fill the tower when it's smelted.
SOLUTION
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ASKER
Then really the tower has:
7,300 tons of Iron
2,500,000 of Rivets
50 tons of Paint
10 tons of Primer
Anyone knows how many cubic meters it is?
7,300 tons of Iron
2,500,000 of Rivets
50 tons of Paint
10 tons of Primer
Anyone knows how many cubic meters it is?
ASKER
7,300 tons of iron is = 843,6 m3
Though rivets, paint and primer is very hard to find.
Though rivets, paint and primer is very hard to find.
SOLUTION
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ASKER
Then the smelted Eiffel Tower will fill: 900 cu.m
So on the 3 pyramid model, how many cubic meters did you come up with?
ASKER CERTIFIED SOLUTION
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Well ..
I guess that assumes you've taken all the air out of the initial volume. So, take the volume that is left after you measure out the size of the iron, and use the density of air to see how much the entire volume would weigh. Air and iron.
Whoa, air is heavy!
I guess that assumes you've taken all the air out of the initial volume. So, take the volume that is left after you measure out the size of the iron, and use the density of air to see how much the entire volume would weigh. Air and iron.
Whoa, air is heavy!
Here ya go:
http://www.pzzls.com/eiffe