Arc Length Formula

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Arc is the distance between two points on a curved surface. Arc length is the measure of the length making the arc on curved or circular path. If A is one point on the circular curve and B is another point on the curve then the arc length AB = r * θ. Here r is the radius of the circle and θ is the angle the arc makes with the center of the circle in radians.  
 
Example 1: Find the arc length of the curve with radius 5 cm which makes a 30° angle with the center.

The length of radius of the given circle, r = 5 cm.
The arc makes a 30° angle at the center.
Change degrees to radians for the given angle.
This gives, (30°/360°) * 2π = 0.52 radians which means angle, θ = 0.52 radians

The length of the arc, s = r * θ.

The length of the arc, s = 5 * 0.52 = 2.6 cm.

 
Example 2: Find the arc length AB on the curve with radius 10 cm which makes a 60° angle with the center.

The length of radius of the given circle, r = 10 cm.
The arc makes a 60°angle at the center.
Change degrees to radians for the given angle.
This gives, (60°/360°) * 2π = 1.05 radians, which means angle, θ = 1.05 radians

The length of the arc, s = r * θ.

The length of the arc, s = 10 * 1.05 = 10.5 cm. 



 

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