NECO 2008 Mathematics · Question 2
A sector of angle 120° is cut out from a circle of radius 13.5cm. what area of the circle is remaining ? (π = )
Options
- A.14.1cm2
- B.95.5cm2
- C.190.9cm2
- D.381.9cm2
- E.763.7cm2
Answer: D. 381.9cm2
Explanation written with AI and checked against the answer key
Analyze the question: A circle of radius 13.5 cm has a 120° sector removed. We need the area of the part left, which is the remaining 240° of the circle. Concept: Area of a sector = (θ/360) × πr² Solution: Full area of the circle: πr² = (22/7) × 13.5 × 13.5 = (22/7) × 182.25 = 4009.5 / 7 ≈ 572.79 cm² Remaining fraction = (360° − 120°)/360° = 240/360 = 2/3 Remaining area = (2/3) × 572.79 ≈ 381.86 cm² ≈ 381.9 cm² Check: the removed sector is (1/3) × 572.79 ≈ 190.9 cm² (option C). That is a trap, because it is the area cut out, not the area remaining. Answer: The remaining area is about 381. Tip: Read the last line of the question carefully. Examiners often include the area of the removed part (here, option C) as a distractor. Quick shortcut: when 120° is removed, 2/3 of the circle remains.AI can make mistakes. Report anything that looks wrong.
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