## FINDING LENGTH OF ARC WITH ANGLE AND RADIUS

Finding Length of Arc with Angle and Radius :

In this section, we will see how to find the length of arc with angle subtended and radius are given.

Length of arc  =  (θ/360)  2Πr

here θ  -  angle formed by two radius

## Finding Length of Arc with Angle and Radius Examples

Example 1 :

Find the length of arc whose radius is 42 cm and central angle is 60°

Solution :

Length of arc  =  (θ/360)  2 Π r

Here central angle (θ)  =  60° and radius (r)  =  42 cm

=  (60°/360)  2  (22/7)  42

=  (1/6)  2  22  6

=  2  22

=  44 cm

Hence the length of arc is 44 cm.

Example 2 :

Find the length of arc whose radius is 10.5 cm and central angle is 36°

Solution :

Length of arc = (θ/360) x 2 Π r

Here central angle (θ) = 36° and radius (r) = 10.5 cm

=  (36°/360)   (22/7)  10.5

=  (1/10)  2  (22/7)  10.5

=  (1/5)  (22/7)  10.5

=  (22/7)  2.1

=  22  0.3

=  6.6 cm

Hence the length of arc  =  6.6 cm

Example 3 :

Find the length of arc whose radius is 21 cm and central angle is 120°

Solution :

Length of arc  =  (θ/360)  2 Π r

Here central angle (θ)  =  120° and radius (r) = 21 cm

=  (120°/360)  2  (22/7)  21

=  (1/3)  2  22  3

=  2  22

=  44 cm

Hence the length of arc  =  44 cm

Example 4 :

Find the length of arc whose radius is 14 cm and central angle is 5°

Solution :

Length of arc = (θ/360) x 2 Π r

Here central angle (θ) = 5° and radius (r) = 14 cm

=  (5°/360)  2  (22/7)  14

=  (1/72)  2  22  2

=  (1/36)  2  22

=  (1/18)  22

=  (1/9)  11

=  11/9

=  1.22 cm

Hence the length of arc = 1.22 cm

After having gone through the problems explained above, we hope that the students would have understood the stuff given on finding length of arc with angle and radius

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