An arc subtends a central angle measuring

2π3/dfrac{2/pi}{3}

3

2π



start fraction, 2, pi, divided by, 3, end fraction

radians.

What fraction of the circumference is this arc?

of the circumference

The arc is one-third of the circumference.

Step-by-step explanation:

The area of a circumference = 2πr

C = 2πr ... (1)

If an arc subtends a central angle measuring 2π/3 rad,

The length of the arc = rθ

Given θ = 2π/3

Length of the arc L = r (2π) / 3

L = 2πr/3 ... (2)

L = 1/3 (2πr)

Since C = 2πr

L = 1/3C

This shows that the arc is one-third of the circumference.