Looks a bit wrong to me. If you had a "room" 6km by 6km the floor area would be 36 square Km, not 12. You'd be looking at a "room" about 4km by 3Km.
Except that you wouldn't. You'd need
far more space than that for several reasons:
1) That volume was an estimate for transistors only. You'd need a lot more space for the wiring to connect the transistors together.
2) Heat generation would also be scaled up. You would need a lot more space to provide sufficient cooling.
3) With hundreds of billions of macroscopic components there would be frequent failures requiring replacement. So you'd need a lot more space to enable people to move around inside the giant CPU in order to replace parts. That would help a lot with the cooling issue, so at least you can kill two birds with one stone there. But you'd still need massive cooling systems. A couple of dozen 120mm fans won't do the trick here
4) You'd need a lot of people to service the giant CPU, so you'd need space to allow for staff transport to and from the site and staff transport within the site. Since it's so big, you'd need internal transport. Small EVs, probably, something like golf carts, so technicians can get to faults in a reasonable amount of time with spares required.
5) You'd need storage space for spare parts too, probably several such storage spaces given the size of the place. Otherwise downtime would be pretty much all the time.
So at a really rough estimate, I'd say if you were restricting your building to 40m tall you'd probably need it to be at least 5Km by 5Km. Probably more. Also, it's probably impossible
in practice to get such a thing to work. You can do it for really simple processors, but not ones with tens of billions of transistors.
Early electrical computers were as you describe, but with tens of thousands of components rather than tens of billions. They filled buildings and required constant staffing by technicians. It's even theoretically possible to construct a computer, a bona fide programmable general purpose computer, that's entirely mechanical. Sir Charles Babbage designed one in the 1830s and called it an Analytical Engine. It was never built because the cost would have been enormous, nobody with control of enough money was absolutely certain it could be built with mid 19th century technology and Babbage kept changing the design to improve it. It's technically possible, though. One of his earlier mechanical processors (Difference Engine number 2) was built in the 1990s and works perfectly well. A few years back there was a project started to build Babbage's Analytical Engine. Presumably it hasn't happened yet. IIRC, they were finding it heavy going trawling through Babbage's surviving notes and sorting out the many revisions he made to his designs in order to get a single complete, compatible and functional design to work from. It would be a bummer to be building version 5 of one part and version 8 of another part and then find out that v8 of the second part was only compatible with v6 of the first part.