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Arc Length Formula

Arc is nothing but a segment of a circle. Arc length is the length of the curved portion that makes up the arc. The arc length is greater than the length of the straight line that can be drawn between the end points of the arc. It is the product of the radius of the arc and the central angle of the arc. The radius of the arc is the radius of the circle of which the arc is a segment. The central angle of the arc is the angle made by the end points of the arc with the center of the circle.

The Arc Length Formula is given as,

Where,
S represents the arc length.
r represents the radius of the arc.
θ represents the central angle of the arc.

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Arc Length Problems

Some solved problems on arc length are given below:

Solved Examples

Question 1: Find the arc length if the radius of the arc is 7 cm and its central angle is 30o ?
Solution:

Given,
Radius of the arc = r = 7 cm
Central angle of the arc = $\theta$ = 30o

Arc length, S
= 2$\pi$r $\times$ $\frac{\theta}{360}$

= 2 $\times$ $\pi$ $\times$ 7 $\times$ $\frac{30}{360}$ cm

= 3.665 cm

Question 2: Find the arc length if the radius of the arc is 15 cm and its central angle is 65o ?
Solution:

Given,
Radius of the arc = r = 15 cm
Central angle of the arc = $\theta$ = 65o

Arc length, S
= 2$\pi$r $\times$ $\frac{\theta}{360}$

= 2 $\times$ $\pi$ $\times$ 15 $\times$ $\frac{65}{360}$ cm

= 17.017 cm

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