Question

MEDAL AND FAN!
Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 3 inches, and the larger gear has a radius of 7 inches.
(will post picture)
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.

Answer 1

is this all correct??
Part 1: An entire rotation (360 degrees) is when the contact with the larger gear 2 * pi * r = 6 * pi. One complete rotation for the smaller gear is 18.84 in.
The larger gear has a wider circumference (2 * 7 * pi).
((6 * pi)/(14 * pi)) * 360 = 154.3 degrees

Part 2: The smaller gear will make 2.33 rotations during one rotation of the larger gear.
14 * pi / 6 * pi = 2.33 rotations

Answer 2

@Kainui