Volume of People

A coworker recently texted me from a conference asking the volume of a sphere that would contain the world's population.  xkcd's "What-if?" has already addressed the area that would be required for everyone to stand (Rhode Island), but now we can stack people.

My question for this was how comfortable the people in my sphere are. There are some seven billion people in the world. In New York City, apartments must be at least 400 square feet, although new "micro-apartments" will be 300 SF.  Let's assume each person on the planet lives in a 300 SF studio. With 8-foot ceilings and two feet of structural floor, that's 3,000 cubic feet per person.  For all seven billion people, we'd need nearly 150 cubic miles of building, so our giant sphere apartment building would be 6.5 miles in diameter.  Let's say 7 miles if we allow for elevators and hallways.

Like the Technosphere, only 100 times as wide

What if the sphere was instead a future spaceship making some trip to another planet or star system? Cruise ship cabins get as small as 85 SF while Amtrak's sleeper rooms are about 50 SF, and both of these can sleep two.  We'll also cut the floor height to 8 feet (with 7 foot ceilings).  Depending on the luxury of travel, our sphere needs to be 2.6 to 3.1 miles across now.  Maybe a little more if we have life support and engines.

Like a Borg sphere scout, but 6 times as wide. Slightly larger volume than a Borg cube, but definitely smaller than a Death Star.

What if the people didn't need to be alive? Instead, let's build a spherical hearse for our 7 billion.  People are all different sizes, but on average, our caskets will be 6' by 2' by 1'.  Now we're really saving room, and can fit everyone on the planet 0.57 cubic miles. Our sphere is just a hair above a mile in diameter.

Like if Harold Chasen got a hold of these concept cars, and also made them 500 times as wide.

"No," my coworker said. "He says it's less than a kilometer."  What??  I've stuffed the people about as tight as I can get them. The only way I can pack them tighter is... oh god.

 Only not with ice.

The volume of a person is about 66 liters, or 2.33 cubic feet.  If you liquefy the human race and pour them into a spherical tank, all of humanity will fit in a diameter of 0.6 miles -- like from the White House to the Washington Monument.

Now we just need to fill that sphere.

I still don't know why my coworker needed this answer.