Problem 831

Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 4 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.





perimeter of the smaller circle = 2π(4) = 8π

in one rotation of the smaller gear, arc created at larger gear = 8π

angle =\frac{8\pi }{2\pi *7} *360
angle =\frac{4}{7} *360
angel = 205.7 degree

perimeter of larger gear = 2π*7 =14π
perimeter of smaller gear = 2π*4 = 8π
rotations make by smaller gear during one complete rotation of larger gear = \frac{14\pi }{8\pi }
= 1.75 rotations.



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