Question 460914
First we find the radius of the circle  with circumference {{{31.4=10*pi}}}:

{{{r=(31.4)/(2*pi)=10*pi/(2*pi)=5}}} radian. As we know the length of the arc is 

given by the formula:{{{l=r*theta}}}, where {{{theta }}} is the angle 150 degree

or {{{5*pi/6}}} radian. Substituting we get:{{{l=5*5*pi/6=25*pi/6}}} radian.