Here's the picture. Earth is beyond saving and is too polluted to be habitable anymore. My plan is to have this ship built on the moon, using materials from our asteroid belt. A bit of a problem is, I'm not exactly sure how big the ship would have to be, and how the size of it affects its functions and speed, but the latter can be a question for another time. If the average density of population ranged anywhere from places such as Manhattan to Manila, and the interior of the ship was laid flat like a boat (layers possible if necessary), along with considering room for necessary crops and creatures needed for survival, about how big would this ship need to be to fit roughly 7 billion people? For around let's say, a century or two?
edit : I appreciate the different input, while I understand it's unrealistic for the damaged to Earth to be irreversible, I would still like something immanent requiring the need of worldwide evacuation, which may need to stem into another question. Flaws in my question have been pointed out, so I'll be sure to work that through. Thank you for all your help :)