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Well first of all it would probably take about 10 years to build at a cost of around 150 to 200 trillion dollars, see something as massive as that would have to be built in orbit and getting into orbit costs a whole butt load of money so you see the problem, a project as massive as that would require funding from several countries and it would have to be a joint international endeavour, you should join the lifeboat foundation if you have a lofty goal of building a massive ship like that, here is a link to there website.
http://lifeboat.com/ex/ark_i
http://lifeboat.com/arki/design-construction.shtml
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