Question

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.

Answer 1

A)circumfrence of smaller gear is 6pi while circumference of larger gear is 14pi. thus 6pi of the 14pi would be turned so 0.4257 of the larger gear would be turned. 0.4257*360 would give us the angle, 154.3 degrees.
B)since the circumference of the larger gear is 14pi in one rotation the smaller gear would have rotated a length of 14pi. Thus 14pi/6pi=2.3 or 7/3 rotations.