SOLUTION: A radius with a gear of 4 inches turns though an angle of 7(pi)/8 radians. WHat distance does a point on the edge of the gear travel as the gear turns through this angle? Round you

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Question 301685: A radius with a gear of 4 inches turns though an angle of 7(pi)/8 radians. WHat distance does a point on the edge of the gear travel as the gear turns through this angle? Round your answer to the nearest tenth.
PLEASE HELP! Show steps so I understand. :((
Found 2 solutions by Alan3354, Fombitz:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A radius with a gear of 4 inches turns though an angle of 7(pi)/8 radians. WHat distance does a point on the edge of the gear travel as the gear turns through this angle? Round your answer to the nearest tenth.
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Or a gear with a radius ....
Using radians makes it easy:
s = r*angle
s = 4*7*pi/8 = 7pi/2 inches
s =~ 11 inches

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Make a circle.
Mark a point on the circumference.
Rotate that circle about its center 360 degrees or 2pi radians.
That point just traveled the full length of the circumference.
Similarly if you rotated any part of a full revolution you could calculate that distance as a portion of the circumference.
Set up a ratio.
Distance traveled is to the circumference as angle is to (2pi).
D%2FC=A%2F%282%2Api%29
D=A%2AC%2F%282%2Api%29
The circumference based on the radius is,
C=2%2Api%2AR=2%2Api%2A4=8%2Api
The angle traveled is,
A=%287%2F8%29pi
Therefore the distance traveled is,
D=%28%287%2F8%29%2Api%2A8%2Api%29%2F%282%2Api%29
D=%28%287%2Fcross%288%29%29%2Api%2Across%288%29%2Across%28pi%29%29%2F%282%2Across%28pi%29%29
D=%287%2F2%29pi or approximately 11.0(10.995) inches.