The perimeter of a minor sector of a circle of radius 5 cm is 15.5 cm. Find the area of the minor sector (use π=).
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Correct answer: B
Explanation
The correct answer is option 2 i.e. 13.75 cm2.
Radius (r) = 5 cm
Perimeter of minor sector = 15.5 cm
Perimeter of sector = arc length + 2 × radius
⇒ Arc length = 15.5 − 2×5 = 5.5 cm
Arc length = (θ/360) × 2πr
⇒ 5.5 = (θ/360) × 2 × (22/7) × 5
⇒ θ = 63°
Now, area of sector = (θ/360) × πr2
= (63/360) × (22/7) × 25
= 13.75 cm2