I'm skeptical of the standard explanations of how the entire population of the world could fit into Delaware/Alberta/the Grand Canyon, and so forth.
Since the Grand Canyon is about 2 miles deep and 10 miles across, this means a 40 mile cross-section of the Grand Canyon should suffice to fit everyone on earth. Kinda leaves a hell of a lot of the planet for supporting that community, no? ...Yeah, but who wants to live in the center of a giant cube, 4 miles from the nearest window? What about hallways, garbage collection, water, waste, air conditioning, and so forth? For starters, a giant cube wouldn't have nearly enough surface area to provide all these things to its inhabitants, and their standard of living would be severely impacted.
For giggles, I’ve drawn a 9 square mile map of my neighborhood. If we equally distributed California’s population, each mile would have to support 1/9 of 35,484,453 or 3,942,717. If we further divide this by 256 and 256 again, we’ll get the number of stories we’ll need, which is about 60.
So, in a little area of my neighborhood in California, if it was sixty 20′ stories tall, is sufficient to house EVERYONE in California in their own 20′ by 20′ by 20′ home. A family of 4 would have 4 of these cubes or 24 10′x10′ rooms!
So how much volume would be needed to house everyone in the way to which we've become accustomed? Well, probably about as much we're currently using. There's already an existing incentive structure that discourages people from spreading too thinly, because as functional density increases so does efficiency. As efficiency rises people become more wealthy. As people become more wealthy they want to live more luxuriously. As people want to live more luxuriously they require more space -- and thus desire a lower functional density.
It's a feedback loop that regulates population rather well, as can be seen in wealthy countries with dropping birth rates. That's the real reason that population growth isn't going to be a problem in the future, not because we could all live in Canyon Cube Condos (or "C-cubeds" as I call them).
Just imagine trying to transport food for 6 billion people into (and the waste from 6 billion people out of) the Grand Canyon. Imagine the damage a single nuke could do, or a brownout