Care for a right answer? I'm running very tight on time, so I'll do the one I can do from my head, then I'll tackle the rest later:
Say the worm's rotational velocity is 1rpm, the worm wheel's velocity is then 1/40rpm. At 1rpm, the edge of the worm wheel is moving at 3/4"/minute because pitch indicates how far you move with one revolution. If you do 1 rpm, the edge moves 3/4" in that minute.
Armed with the rotational velocity of the worm wheel (1/40rpm) and the edge velocity (3/4"/min.) we can calculate the diameter of the wheel.
The formula for radius using edge velocity and rotational velocity is:
v=omega*r, where omega is your rotational velocity.
Put in the numbers and do your units bookkeeping:
3/4"/min = 1/40 rpm * ((2*pi rad/min)/1rpm) * r
Put everything on the left side:
4.775" = r
D = 2r, so D = 9.55", your answer is a.
A note to gerdb: stay away from the philosophy books, and pay more attention to your engineering texts...