Determine the arc length of a sector with a radius of 9cm and a central angle of 0=5pi/6 radius

Question

Determine the arc length of a sector with a radius of 9cm and a central angle of 0=5pi/6 radius

Answer 1

•m∠θ = 5π/6 ← given

r = 9 (cm) ← given

C = 2πr → circumference of a circle

2π → the measure of the central angle of the full circle

Let "x" be the length of the arc, cut out by ∠θ.

Making a proportion:

2πr/2π = x/(5π/6)

x = 5πr/6 = 5 • π • 9/6 = 23.56 (cm)

Answer 2

arc length = radius * central angle in radians = 9 cm * 5pi/6 radians = 45/6 cm = 7.5 cm