What is the area of the region enclosed by three identical circles (each of radius 4 cm) touching each other?
- A. \frac{8\pi}{3} square cm
- B. (16\sqrt{3}-\frac{8\pi}{3}) square cm
- C. (16\sqrt{3}-8\pi) square cm ✓
- D. \frac{16\pi}{\sqrt{3}} square cm
Correct Answer: C. (16\sqrt{3}-8\pi) square cm
Explanation
The centers form an equilateral triangle of side 8 cm. The area enclosed is Area(triangle) - 3 \times Area(sector). Triangle area = \frac{\sqrt{3}}{4}(8^2) = 16\sqrt{3}. The 3 sectors (60^\circ each) equal half a circle: \frac{1}{2} \pi (4^2) = 8\pi. Result = 16\sqrt{3}-8\pi.
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