Question

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

Answer 1

The arc is one-third of the circumference.

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.