Part 1:
The circumference of the smaller circle is...
C = 2*pi*r
C = 2*pi*2
C = 4*pi
The circumference of the larger circle is...
C = 2*pi*r
C = 2*pi*8
C = 16*pi
The ratio of the two circumferences is
16*pi:4*pi = 4:1
which means that for every single full rotation of the larger gear, the smaller gear will complete four rotations
If we flip things around, we will have the ratio 4:1 turn into 1:0.25 (divide both parts by 4). Now this says that for every single rotation of the smaller gear, the larger gear rotates 1/4 or 25% of the larger circle circumference.
1/4 of 360 degrees is 90 degrees
So the larger gear will rotate 90 degrees when the small gear completes a full revolution.
Answer: 90 degrees
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Part 2:
This was pretty much answered in part 1 above. The answer here is 4. The circumference of the larger gear is 4 times larger (since the radius is 4 times larger), so the gear ratio here is 4:1.
Answer: 4
