So, somewhat inspired by earlier suggestions of not calculating the surface area of Hive Sibellus, I decided to not only do that, but also to take a look at the population figures. The result is of course that these things don't add up, and that the information given is contradictory.
The facts, as given in the Dark Heresy Core Rulebook:
Populations:
Planet Scintilla: 25 billion (p290)
Hive Sibellus: 2x population of Hive Tarsus (p293)
Gunmetal City: "For now, it is a 4 billion strong foundry station" (298)
Ambulon: "Ambulons equivalent of midhivers are the hundreds of thousands of workers…" (p297)
Wilderness: Unknown
The population of Sibellus then, is 2/3 of what remains of Scintilla’s population when we subtract GMC, Ambulon and the wilderness.
Lets assume the population of Ambulon is 1 million. Mid-hivers make up the largest part of a hives population, and they are numbered in the 100 000's, so 1 million seems reasonable. Lets also assume that the wilderness is not part of the equation. This gives:
2/3 * (25 - 4 - 0.001) = 2/3 * 20,999 = 14 billion (almost).
Dimensions:
“The hives themselves are astonishingly large …. cover continents and stretch for miles into the sky” (p 16)
Sibellus: "8000 kilometre-wide bulk", "skirts touch the coast itself - a 500 kilometre belt"
At most, this makes a circle with diameter 8000 Km. This results in a surface area of 50 240 000 Sq.Km
However, the hive is probably not circular, but shaped more like an oval, oblong shape, where 8000 is the longest diameter.
The silhouette figure of Sibellus in Purge The Unclean (p 32) shows Sibellus to be higher than it is wide (by a factor of about 1,1). Obviously, Sibelus cannot be over 8000 Km tall. The International Space Station is in orbit some 350 Km above earths surface.
So I conclude that the picture either shows Sibellus from “side view”, showing the narrow side of a hive shaped like a long sausage, or is very wrong in its depiction.
If we assume an elliptical shape, 3000 Km thick across the narrow side, this gives a SA of 18 840 000 Sq.Km
By comparison, Europe has a SA of 10 180 000, and North america has 24 490 000 (Wikipedia.com)
So, we have a massive Hive, covering an Area larger than Europe, with a population of more than twice that of our Earth.
So far so good. The problem comes when we look at population densities.
4 Billion people spread across 18,8 million sq.km, gives a population density of 743 people/Sq.km
By comparison, New York City has a density of 10 000 people/sq.km, and Mumbay heads the charts at 22 658. These are packed city centers, but still have parks and open areas. Not even close to Hive-density.
The Hive is described as a crowded place, and I feel it should easily be as crowded as our most crowded cities here on earth today. However, put a density of 20 000 over an area of 18,8 million sq.km and you end up with 376,8 Billion, and thats just on "ground level".
I don't know how many levels Hive Sibellus has "on Average", but I'd Imagine at least 3 (probably a lot more). That gives 1,1 Trillion people.
Which puts Tarsus at 565 Billion, and Scintilla total at 1,7 Trillion people. Almost.
That’s a lot of people
And would require massive food imports. It's also a far cry from the stated 25 billion.
If we were to keep the population size, and calculate area based on a density of 20 000, the resulting SA is a mere 700 000 sq.km. A circle less than 1000 km across.
So which is right? The Size, or the population numbers?