2015 · Q89
From a circular piece of cardboard of radius 3 cm, two sectors of 40° each have been cut off. The area of the remaining portion is
Elementary MathematicsMensuration
- A11 square cm
- B22 square cm
- C33 square cm
- D44 square cm
Explanation
This is a sector-area problem: the area of a sector of angle θ in a circle of radius r is (θ/360°)·πr². The two cut-off sectors remove 40° + 40° = 80°, so the remaining cardboard subtends 360° − 80° = 280° at the centre. With r = 3 cm the remaining area is (280/360)·π·9 = 7π ≈ 7 × 3.14 = 22 cm². Hence option (b). The distractors correspond to miscomputing the remaining angle: 11 cm² comes from treating the remaining sector as 140°, and 33 or 44 cm² from adding rather than subtracting the removed portions.