Hi, please help it's on arc length and sectors

Question

1. If a sector has an area of 16pi/3in² and a central angle of pi/6 radians, what is the radius of the circle?
2. If a sector has an arc length of 10pi/3in and a radius of 10 inches, what is the central angle?

Answer 1

1) A full circle of arc length 2π radians has and area of πr². We can form a ratio:

2π/(π/6) = πr²/(16π/3)

12 = 3r²/16

r = √(16•12/3) = 8 in

2) Arc length, S = rθ

θ = S/r = (10π/3)/10 = π/3 radians or 60°

Answer 2

Area of sector=91/2)*theta*r^2, theta is measure of angle and r is value of radius.

.

when theta=pi/6

16pi/3 in^2=(1/2)*(pi/6)*r^2

multiply both sides by 12

64 in^2=r^2

8 in=r

Arc length=theta*r, theta is angle measure and r is value of radius

10pi/3 inches=theta*10 inches

divide both sides by 10 inches

pi/3 radians=theta