Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 2 inches, and the larger gear has a radius of 8 inches.

Part 1: What is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation?

Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear?

Show all work.

In this question, the gears are connected to each other their perimeter. This will cause the distance of rotation for both gears will be the same. But the gear A is bigger, thus having a higher perimeter.

Part 1:
A full rotation or 360 degrees rotation will have a value of 1 perimeter. Then, we can determine the distance from gear B rotation and find out how much the gear A move distance

gear A distance= gear B distance
gear A distance= 1 * (22/7) * 2 *2

If the distance converted into degrees, then:
gear A rotation= gear A distance/ gear A perimeter * 360°
gear A rotation= (22/7) * 2 *2/ {(22/7) * 8 *8} * 360°
gear A rotation= (1/16) * 360°= 22.5 degrees

Part 2:
The problem is similar to part 1 but the number is reversed.

gear B distance= gear A distance
gear B distance= 1 * (22/7) * 8 *8

gear B rotation= gear B distance/ gear B perimeter
gear B rotation= (22/7) * 8 *8/ {(22/7) * 2 *2} = 16 rotation