A solid sphere of diameter 60\text{ mm} is melted to stretch into a wire of length 144\text{ cm}. What is the diameter of the wire?

Explanation

Radius of sphere = 30\text{ mm} = 3\text{ cm}. Volume of sphere = \frac{4}{3}\pi(3)^3 = 36\pi\text{ cm}^3. Volume of wire (cylinder) = \pi r^2 h = \pi r^2(144). Equating them, 144\pi r^2 = 36\pi \implies r^2 = \frac{1}{4} \implies r = 0.5\text{ cm}. The diameter is 2r = 1\text{ cm}.

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