A chord of a circle of radius 10 cm subtends an angle of 90° at the center. What is the area of the minor segment bounded by this chord? (Take π = 3.142)
Answer and explanation
Correct answer: C. 28.55 cm²
- Step 1: Area of minor sector = (90° / 360°) × π r² = 0.25 × 3.142 × 10² = 0.25 × 314.2 = 78.55 cm². Step 2. Area of right isosceles triangle = 0.5 × r × r = 0.5 × 10 × 10 = 50.00 cm². Step 3. Area of minor segment = Area of sector - Area of triangle = 78.55 - 50.00 = 28.55 cm². Answer: 28.55 cm². Why not the others: 78.55 cm² is the sector area alone; 50.00 cm² is the triangle area alone; 39.28 cm² halves the sector area.
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