an air plug on a bike is 15 inches from the center of the bike. if the wheel is spun 315 degrees clockwise, how far does the air plug travel?

We can find distance along a circle if our measurements are in radians. So... 

 

If we multiply both sides by 315 and simplify we see that 315 degrees is 

 


Now using the arclength formula we compute: 

 
which is about 82.47 inches 


:)