What are the exact dimensions of a 9 ft pool table after it is assembled?

The short answer:

nineteen feet by fifteen feet (19' x 15')

The long answer:

A nine foot pool table, 9' x 4'6" (108" x 54"), has a playing area of 8'4" x 4'2" (100" x 50"). Most cue sticks are 58" in length.

To determine the minimum room size without any interference you should first add a stroke distance to the cue length (6" is a good minimum stroke distance), ie 58" cue + 6" stroke = 64".

To calculate the minimum dimensions for the room just add twice the cue/stroke length to each of the playing area dimensions.

100" + (2 x 64") = 100" + 128" = 228"

50" + (2 x 64") = 50" + 128" = 178"

And there you have it! A reasonable minimum size room for a nine foot table is 228" x 178" or 19' x 14'10"

PS. I'd much rather play on an old worn out bar size table that actually fits in the room, than even the nicest fanciest tournament table if there's not enough room to shoot.