if you have a set on the flop, you will fill up just 28% of the time.
Actually, you will fill up 29.1% of the time. You will fill up or make quads 33.4% of the time.
You don't often see the calculation of the odds for filling up or making quads starting from a set. Earlier I gave
3 methods of computing the odds for completing a draw. This problem uses one of the alternative methods (method 2). We are calculating the odds for the board pairing again, but if it doesn't pair on the turn (7 outs) we have 3 additional outs to pair on the river (10 outs) because then we can pair the turn card.
7/47 + 40/47 *10/46 = 33.4%