How To Find Arc Length

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We know Arc is a segment of a circle. In other words we can say Arc is a curve.  We Know Arc length is the distance along the curved line. We can say length of an arc is the part of the circumference. We can call the angle which is made by the end points of the arc with centre as central angle.

We know the formula to find the arc length that is

Arc length = (Ø/ 360o) x 2πr

Here, r is the radius and

Ø is the central angle.

Example 1: Find the arc length if the radius of the arc is 8 cm and its central angle is 30o.
 
Solution: We can write

r = radius of the arc = 8 cm

ø = central angle = 30o

The formula to find arc length = (Ø/ 360o) x 2πr

We can plug the r and Ø values in the above formula. Then we have

arc length = (30o/360o) x 2 (22/7) x 8

= (1/ 12) x 16 x (22/7)

= 4.19 cm

Example 2: Find the arc length of a circle with diameter 12 cm and the central angle 180o.
 
Solution: from the problem, we can write

r = radius of the arc = (1/2 ) diameter = (1/2) x 12 cm = 6 cm

Ø = central angle = 180o

The formula to find arc length = (Ø/ 360o) x 2πr

We can plug the r and Ø values in the above formula. Then we have

arc length = (180o/360o) x 2 (22/7) x 6= 18.85 cm
 

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