FINDING LENGTH OF ARC WITH ANGLE AND RADIUS

Length of arc  =  (θ/360)  2πr

here θ  -  angle formed by two radius

r  -  radius

Example 1 :

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

Solution :

Length of arc  =  (θ/360) x 2πr

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

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 2πr

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

Example 3 :

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

Solution :

Length of arc  =  (θ/360)  2πr

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

Example 4 :

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

Solution :

Length of arc = (θ/360) x 2πr

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

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