Find Central Angle in terms of pi

Question

Arc Length= 18

radius= 6

In solving for Central Angle I would think of S=r(theta) and plug in those values.

18=6(theta) Theta= 3

Is my thinking even correct and how do i find the central Angle in terms of pi?

Thanks,

Brian

Answer 1

3 is the number of degrees

you can solve the problem as follows or multiply 3*57.2958° to get 171.8874° because 1 radian=57.2958° and work from here, or...

C=2*∏*r

C=12∏

C=12*3.14159

C=37.699

18/37.699=0.477466 of the circumference

0.477466*360=171.88785°

(171.88785/180)∏=0.9549325∏ (round as needed)

Answer 2

You have solved for the central angle correctly - it is 3 radians, which is 3/3.14159 PI = 0.955 PI.