You also have to take into account that the full breadth of the Federation's borders which are in 3-D space. There's a Z-Axis measurement that people tend to forget about when discussing planetary & star system borders across light-years.
The 8,000 LY measurement figure could be the approximate diagonal from the "lowest" 'corner' of Federation space to the "highest" point 'furthest' away.
*(Kind of like using the diagonal measurement of a TV screen when describing it's overall "size")
Technobuilder, good point!