Four circular coins of equal radius are placed with their centres coinciding with four vertices of a square. Each coin touches two other coins. If the uncovered area of the square is 42 \text{ cm}^{2}, then what is the radius of each coin? (Assume \pi=\frac{22}{7})
- A. 5 cm
- B. 7 cm ✓
- C. 10 cm
- D. 14 cm
Correct Answer: B. 7 cm
Explanation
The side of the square is 2r. The uncovered area is the square's area minus 4 quarter circles: (2r)^2 - \pi r^2 = r^2(4 - \pi). Setting this to 42 gives r^2(4 - \frac{22}{7}) = 42 \Rightarrow r^2(\frac{6}{7}) = 42 \Rightarrow r^2 = 49, meaning r = 7 \text{ cm}.
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