Find the length of the arc on a circle of radius r intercepted by a central angle θ.

Solution:

The length of an arc depends on the radius of a circle and the central angle θ.

When angle θ = 360°(2𝜋), the arc length is equal to circumference.

The proportion between angle and arc length is constant,

⇒ S/θ = C/2π

Where, S = arc length and C = circumference of circle = 2πr

⇒ S/θ = 2πr/2𝜋

⇒ S/θ = r

⇒ S = r × θ

Therefore, the length of arc is S = r × θ.

Find the length of the arc on a circle of radius r intercepted by a central angle θ.

Summary:

The length of the arc on a circle of radius r intercepted by a central angle θ is S = r × θ.