Area of a sector of central angle 120° of a circle is 3π cm2. Then the length of the corresponding arc of this sector is
(A) 5.8cm
(B) 6.1cm
(C) 6.3cm
(D) 6.8cm
Answers
Answer:
answer is 6.3
Step-by-step explanation:
area of sector = thita/360° πr2 = 3π
120°/360° πr2 = 3π
πr2/3 = 3π
r2= 3 x 3 {π is canceled as it is on both sides}
r=9
arc of sector = thita /360° × 2 πr
= 120° / 360° x 2πr
= 1/3 x 2 x 22 / 7 x 9
= 44 /7 = 6.8 approx.
Given: Area of a sector of central angle 120° of a circle is 3π cm².
To Find : The length of the corresponding arc
Solution:
Sector is the area enclosed by arc and two radii
Sector area = (sector angle / 360°)πr²
= (120° /360°) πr²
= (1/3) πr² cm²
Equate with given sector area 3π cm².
=> (1/3) πr² = 3π
=> r² = 9
=> r = 3
Hence radius is 3 cm
Arc length = (sector angle / 360°)2πr
= (120° /360°) 2π(3)
= (1/3) 2π(3)
= 2π
= 2 * 3.14
= 6.28
≈ 6.3 cm
the length of the corresponding arc of this sector is 6.3 cm
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