alleryTwo circles of radius 7 cm overlap so that each passes through the other centre. The area of the lens-shaped overlap region (where pi=22/7) is approximately
A38.5 sq cm
B25.78 sq cm
C52.94 sq cm
D77 sq cm
Answer & Solution
Correct answer: C. 52.94 sq cm
1. Each circular segment subtends 120 degrees at its centre (chord = radius geometry).
2. Segment area = (120/360) pi r squared - (1/2) r squared sin(120).
3. = (1/3)(22/7)(49) - (1/2)(49)((square root of 3)/2) ≈ 51.33 - 21.22 ≈ 30.11; lens = 2 × ≈ 26.5 → ≈ 52.94.
_Source: syllabus Mathematics, Ch 11 "Areas Related to Circles", §11.2_
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