JohnWDailey - Again I say there is a big difference between Dwarf and Goblin/Orc underground architecture in the books and in the Peter Jackson movies.
Suppose that Moria had a population of 1,000,000 Dwarves at its height.
Using farming techniques 2,350 persons could be fed with the yield in sweet potatoes from one square kilometer of land. 425.53 square kilometers of land would be needed to feed 1,000,000 Dwarves - equal to an area 20.62 by 20.62 kilometers. Suppose that Moria had a series of chambers 5 kilometers by 5 kilometers square, stacked one on top of another with 100 meters between each level. 20 levels would reach 2 kilometers high and would contain 500 square kilometers of farmland, more than enough to feed a million Dwarves and occupying a small fraction of the volume of a typical mountain.
Supposedly we could feed 13,300 people per square kilometer using hydroponics. Thus 75.187 square kilometers would be needed to feed 1,000,000 Dwarves. That would require three or four farming chambers 5 kilometers by 5 kilometers square, stacked one on top of another with 100 meters between each level for a total height of 300 or 400 meters.
Using aeroponics it might be possible to feed 49,210 persons per square kilometer, thus requiring 20.32 square kilometers. So 21 chambers one kilometer by one kilometer stacked on top of each other with 100 meters between levels should reach 2.1 kilometers tall and provide more than enough food for 1,000,000 Dwarves.
How many people can you feed per square-kilometer of farmland?1
But what about sunlight for growing crops inside a mountain?
The Fellowship of the Ring, Book Two, Chapter Four "A Journey in the Dark" has Gimli sing "The Song of Durin" about Durin the Deathless. The third stanza says:
A king he was on carven throne
In many-pillared halls of stone
With golden roof and silver floor
And runes of power on the door.
The light of sun and star and moon
In shining lanps of crystal hewn
Undimmed by cloud or shade of night
There shone for ever fair and bright.
Gimli seems to be singing that the ancient Dwarves had artificial lighting. With artificial lighting they could light their underground farms to grow food inside the mountains.
And the dwarves could have farmed land outside, in lands claimed by their kingdom. Maybe the Dwarves used a thousand square kilometers of outside farmland to feed a million Dwarves in Moria at its height. That would equal a square areas 31.62 by 31.62 kilometers, or a circular area with a radius of 17.84 kilometers and a diameter of 35.68 kilometers.
And when Dwarf economies were flourishing the Dwarves didn't grow much of their food supplies but traded their goods for food supplies from Elves and Men.
Thus the Dwarves didn't need to hollow out vast volumes under the mountains to grow food. Thus the underground cities of the Dwarves would need to be the size of Human cities and not the size of Human cities plus the farmland necessary to feed the populations of those cities.
The city of Philadelphia, Pennsylvania has a land area of 347.52 square kilometers and an estimated population of 1,567,872 and a density of 4,511.61 persons per square kilometer. Thus if Moria had 1,000,000 Dwarves and Philadelphia's population density it would have 211.65 square kilometers of floor space in it's chambers.
This equals a single level with a square 14.54 by 14.54 kilometers, or a hundred levels each 1.45 by 1.45 kilometers.
If the height of the chambers averaged 10 meters, the total volume of Moria's chambers might be 2.1165 cubic kilometers. And a typical mountain might have a volume on the order of 100 to 1,000 cubic kilometers, for example.
Thus the excavated volume of a Dwarf city in the novels should be only a tiny fraction of the volume of the mountain it is in.
The Dwarf and Orc underground realms in the movies are a different story.
In the movies it often looks like 90 percent of the volume of the mountain has been excavated for the underground city, a very unsafe thing to do. The mountain would probably collapse, crushing everyone in the underground city to death, long before it was excavated that much.
A better method to build an underground city that was mostly empty space instead of rock would be to tear down a Mountain A and transport all it's materials to another place and then build a building B that is the size of a mountain. And when the gigantic building is complete disguise the outside so that it looks sort of like a very regularly shaped mountain.
Of course in a giant, mountain sized building, the interior architecture and placement of supports would have to be very regular and symmetrical, and in the LOTR movies the interiors of Dwarf and Orc underground cities often seem very irregular and natural looking, which is very implausible.
And after seeing three questions in this series, I have the feeling that my answers about plausibility are going to be patterned something like yes, yes, no, yes, yes, no,...for the novels and no, no, yes, no, no, yes,... for the movies.