Question

Can someone check my work?

Answer 1

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 2

so what i did first was find the circumference of both gears

\[2\pi r= 2\pi 3 = 18.84\]
\[2\pi r = 2\pi 7 = 43.98\]

Answer 3

then subtracted to find how much of the big gear was covered in one rotation of the small gear
43.98-18.84=25.14

Answer 4

Then used the arc length formula
\[s=r \theta = 25.14 = 7(\theta)\]

Answer 5

\[25.14/7 = \theta = 3.59\]

Answer 6

@Michele_Laino Did i do this right?

Answer 7

@Hero @Nnesha @Preetha

Answer 8

Nevermind! I see what I did wrong

Answer 9

2pir=2pi3=6pi
2pir=2pi7=14pi
(6pi/14pi)(360)=(3/7)360=0.4286(360)=
154.29 degrees

Answer 10

Hint:
here we can use this general formula:
\[\Large \frac{N}{n} = \frac{3}{7}\]
where N is the number of rotations of the larger gear, whereas n is the number of rotations of the smaller gear