The diameter of a copper solid sphere is 6 \text{ cm}. The sphere is melted and recast into a wire. If the diameter of the wire is 0.5 \text{ cm}, then what is the length of the wire ?
- A. 5.24 \text{ m}
- B. 5.36 \text{ m}
- C. 5.76 \text{ m} ✓
- D. 5.96 \text{ m}
Correct Answer: C. 5.76 \text{ m}
Explanation
Volume of the sphere is \frac{4}{3}\pi(3)^3 = 36\pi \text{ cm}^3. The wire forms a cylinder with radius 0.25 \text{ cm}. Equating volumes: \pi(0.25)^2 h = 36\pi. Thus h = \frac{36}{0.0625} = 576 \text{ cm} = 5.76 \text{ m}.
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