Question

In a circle with a radius of 3 ft, an arc is intercepted by a central angle of 2π/3 radians. What is the length of the arc?

Answer 1

(2/3) PI radians = 120 degrees
If radius is 3 feet then circumference = 2* PI * 3 =
18.8495559215 feet
120 degrees is (1/3) of a circle so the arc length = 18.8495559215 / 3 =
6.2831853072  feet

Source:
http://www.1728.org/radians.htm

Answer 2

Answer:

Hence, the arc length is 2π feet or 6.28 feet.

Step-by-step explanation:

In a circle with a radius of 3 ft, an arc is intercepted by a central angle of 2π/3 radians.

If the central angle is measured in degrees than the arc length is given by:

arc length=(θ\360°)×2πr.

and if central angle is measured in radians than the arc length is given by:

arc length=θr. ( where r is the radius of the circle)

where θ is the central angle.

Hence, here we have:

r= 3 ft.

and θ=2π/3.

Hence the arc length is given by:

Arc length=(2π/3)×3=2π  feet.

Hence, the arc length is 2π feet or 2×3.14=6.28 feet.