What is the area of the region enclosed by three identical circles (each of radius 4 cm) touching each other?
A.16√3 - 8π/3 square cm✓ Correct
B.16π/√3 square cm
C.16√3 - 8π square cm
D.8π/3 square cm
Explanation
The triangle joining centers has side 8, area = √3/4 × 64 = 16√3. Three sectors of 60° each = (1/2)·π·16 = 8π/... total sector area = 3·(60/360)·π·16 = 8π. Enclosed area = 16√3 - 8π. Hmm matches (c)? But area between circles = triangle - 3 sectors. Each sector has 60° in triangle, total = πr²/2 = 8π. So 16√3 - 8π. Answer is (c).
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