3 1/3 is correct, but are you sure you want the block to be 8.5" finished? You mentioned that you thought three 3" strips would give you 8" finished, but that's incorrect; each 3" strip would be 2.5" finished, so you would get a 7.5" finished block, 8" unfinished.
For any FINISHED block size, if you want a 9-patch you need to divide the FINISHED block size by 3, then add 1/2 to get the strip size. Conversely, for any strip size, subtract 1/2 and then multiply by 3 to get the FINISHED 9-patch block size. For instance, for an 9" FINISHED block you need to divide 9 by 3 (giving 3) and add 1/2 (giving 3 1/2).
8.5 is a very unusual size for a finished block. Nothing really goes into 8.5 very nicely. If you look at Marcia Hohn's Quilter's Cache site, you won't see any blocks that are 8.5".