To obtain the length of an arc, what fraction is multiplied by the circumference of a circle (c = 2πr)? b. pi over 180 a. pi over 360 c. radius over 360 d. central angle over 360

The length of an arc is a portion of the circumference of the circle, and the circumference itself can be considered as a full arc length. The arc length is usually represented by letter 's'. To get the arc length, we must get the proportion of the arc measure and arc length. 

Arc measure   =   Arc length
       360º          Circumference

Cross multiply and transpose to get the arc length's formula. Since arc measure is equal to the central angle that intercepts the arc, we can replace arc measure to central angle.

Letter D - central angle over 360
                         
   Arc length = Central angle   x   Circumference
                              360º

The arc length by definition is given by:
 s = r * theta
 Where,
 r: radius of the circle
 theta: central angle in degrees
 Substituting values we have:
 s = 2πr * (theta / 360)
 
 D. central angle over 360

The correct one is c.