Find the length of an arc with a radius of 10.0 m swept across 100 degrees?

The "length of an arc" can be found using:

##s = rtheta##

where ##s## is arc length, ##r## is the distance to the axis of revolution, and ##theta## is the angle swept through.

Converting ##100^o## to radians:

##100^o xx (pi "rad")/(180^o) = (5pi)/9 "rad"##

And now just plug it in:

##s = ("10.0 m")((5pi)/9 "rad") = color(blue)((50pi)/9 "m")##