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. 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.

Circumference of a circle is C = 2πr.

part 1)

so the radius of the smaller gear is 3 inches, so after a full rotation, namely a revolution, the smaller gear has covered an arc of 2π(3), or 6π.

what angle has the larger gear of 7 inches in radius, has it covered with an arc of 6π?



part 2)

since the larger gear has a radius of 7, in a revolution it will have an arc of 2π(7), or 14π.

now, we know the smaller gear does a 6π arc in a revolution, how many revolutions will it do in an arc of 14π?