Take those numbers cum gano salis. I rushed through it. No time right now, but a few simplifying assumptions, a person occupies 1000 cubit feet. This is pretty cramped and does not include space for him to walk or exercise or what have you. The volume of a sphere is V=4/3 pi r^3. Say pi=3, so V ~ 4 r^3. The radius of Earth ~ 4000 miles, with approximately 5K feet in a mile, so the radius of Earth is about 2e7, or 20 million feet. Cubing this is 8e21.

We're looking for volume of new sphere - volume of old sphere = 3e45008 * 10^3, where old sphere is the Earth.

Sphere is not a bad approx, of course, though it's technically a 'geoid' or an 'oblate spheroid.' We'll also assume we'll build over the oceans, as well.

4 (R^3 - 8e21) = 3e45011
R^3 = .75e45011 - 8e21 = 75e45009 - 8e21
The 8e21 is minuscule with respect to the rest, but let's just get rid of the 9.
R^3 = 75e45000
R = (75e45000)^(1/3)
R = 4.2e15000 feet ~ 1.4e15000 meters.

For comparison, it takes, I think, 8 minutes for light to get to Earth from Sol. 8 minutes is 480 seconds (say 500 to make it simple) at 3e8 meters per second, so light travels about 1500e8m= 1.5e11m. Wikis says the distance is 149,597,870,691 meters. We are surprisingly close for so many simplifications. So this extends well past the sun, even the solar system, and probably the galaxy. Still, you should check the math on my earlier msg. The 3e45008 seems suspiciously high. I probably screwed something up.