Arc and Sectors

Question

Find the radius of a circle on which a central angle measuring 5π65π6 radians intercepts an arc on the circle with a length of 35π35π centimeters.

Answer 1

an arc has measure 5∏/6 radians

the arc has length 35∏

L=q/180 * ∏ * r where L=35∏, q=5∏/6 or 150º and r=radius

substitute

35∏=(150/180)∏r

divide both sides by ∏ and simplify 150/180

35=(5/6)r

multiply both sides by 6/5

(6/5)(35)=(6/5)(5/6)r

42=r

r=42 cm