HOW TO FIND THE LENGTH OF ARC OF A CIRCLE

Length of arc  =  (θ/360) x 2πr

here θ  -  angle formed by two radius

r  -  radius

Question 1 :

Find the length of arc whose radius is 28 cm and central angle is 90°.

Solution :

Length of arc  =  (θ/360) x 2πr

Here central angle (θ)  =  90° and radius (r) = 28 cm

  =  (90°/360) ⋅ 2 ⋅ (22/7) ⋅ 28

  =  (1/4) ⋅ 2 ⋅ 22 ⋅ 4

  =  2 ⋅ 22

  =  44 cm

Question 2 :

Find the length of arc whose radius is 14 cm and central angle is 288°.

Solution :

Length of arc  =  (θ/360) ⋅ 2πr

Here central angle (θ) = 288° and radius (r) = 14 cm

  =  (288°/360) ⋅ 2 ⋅ (22/7) ⋅ 14

  =  (144/180) ⋅ 2 ⋅ 22 ⋅ 2

  =  (72/90) ⋅ 2 ⋅ 22

  =  (72/45) ⋅ 2 ⋅ 22

  =  (72 ⋅ 22 ⋅ 2)/45

  =  3168/45

   =  70.4 cm

Question 3 :

Find the length of arc whose radius is 10.5 cm and central angle is 45°.

Solution :

Length of arc  =  (θ/360) x 2πr

Here central angle (θ) = 45° and radius (r) = 10.5 cm

  =  (45°/360) ⋅ 2 ⋅ (22/7) ⋅ 10.5

  =  (9/72) ⋅ 2 ⋅ 22 ⋅ 1.5

  =  (1/8) ⋅ 2 ⋅ 22 ⋅ 1.5

  =  (1/4) ⋅ 22 ⋅ 1.5

  =  (1/2) ⋅ 11 ⋅ 1.5

  =  8.25 cm

Question 4 :

Find the length of arc whose radius is 35 cm and central angle is 18°

Solution :

Length of arc  =  (θ/360) x 2πr

Here central angle (θ)  =  18° and radius (r) = 35 cm

  =  (18°/360) ⋅ 2 ⋅ (22/7) ⋅ 35

  =  (1/20) ⋅ 2 ⋅ 22 ⋅ 5

  =  (1/10) ⋅ 2 ⋅ 22 ⋅ 5

  =  (1/2) ⋅ 2 ⋅ 22 

  =  11 cm

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