how can we prove that length of arc in a circle is equal to radius of circle multiplied by angle between extreme radii or sector?
for a central angle in a circle, its radian angle measure, $\displaystyle \theta $ , is defined as the ratio of the length of the intercepted arc, $\displaystyle s$ , divided by the length of the radius, $\displaystyle r$ ...
$\displaystyle \theta = \frac{s}{r}$
using that definition, you should be able to arrive at the desired result rather easily.