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)##