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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