Finding Radius and Central Angle "in terms of pi"

Question

I do want to first thank those that helped with this concept, though importantly, I am trying to understand how to solve such a problem "in terms of pi". Here are 2 problems:

1.

Arc Length= 38

Central Angle= 128 Answer given: 855/16pi

Radius= in terms of pi?? Of course I am looking for the how?

2.

Arc Length=18

Radius=6 Answer given: 540/pi ????

Central Angle= interns of pi

Answer 1

central angle=128°

128 is what part of 360 ?

128/360=16/45

128 is 16/45 of 360

arc length is 38

38 is 16/45 of the circumference

38=16/45*C

C=38*(45/16)

C=1710/16

C=2∏r

set them equal to each other

1710/16=2∏r

divide both sides by 2∏ to get r

r=(1710/16)/2∏

r=(1710/16)*(1/2∏)

r=1710/32∏

r=855/16∏

C=2∏r

C=2∏6

C=12∏

18 is what part of the circumference ?

18/12∏

3/2∏

now find the angle

(3/2∏)*(360)=

(3/∏)*(180)=

540/∏ radians