Multiple choice

A solid sphere of diameter 12 cm is melted and draw into a wire of radius $\displaystyle \frac{1}{5}cm$ then the length of the wire is

  1. 108 m

  2. 72 m

  3. 84 m

  4. None
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B Correct answer
Explanation

Volume of sphere = (4/3) * pi * r^3 = (4/3) * pi * 6^3 = 288 * pi. Volume of wire = pi * r^2 * h = pi * (1/5)^2 * h = pi * h / 25. Setting them equal: 288 * pi = pi * h / 25, so h = 288 * 25 = 7200 cm = 72 m.

AI explanation

When a solid is melted and recast, its volume remains constant, meaning the volume of the sphere equals the volume of the wire. The volume of the sphere is (4/3) * pi * (6)^3, and the volume of the wire is pi * (1/5)^2 * L. Equating the two gives (4/3) * 216 = L / 25, so L = 7200 centimeters. Converting this to meters gives a wire length of 72 m.

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