The diameter of a sphere made of copper is 3 cm. The sphere is melted and recast into a wire. If the length of the wire is half metre, then what is the diameter of the wire?
- A. 0.3\text{ cm}
- B. 0.45\text{ cm}
- C. 0.6\text{ cm} ✓
- D. 0.75\text{ cm}
Correct Answer: C. 0.6\text{ cm}
Explanation
Volume of the sphere = \frac{4}{3}\pi (1.5)^3 = 4.5\pi\text{ cm}^3. Volume of the cylindrical wire = \pi r^2 h = \pi r^2(50). Equating volumes: 50\pi r^2 = 4.5\pi \implies r^2 = 0.09 \implies r = 0.3\text{ cm}. The diameter is 2r = 0.6\text{ cm}.
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