Multiple choice

A sphere made of copper with radius 3 cm, is melted into a wire of diameter 0.2 cm. What is the length of the wire (in m)?

  1. 36

  2. 34

  3. 28

  4. 24
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A Correct answer
Explanation

Volume of sphere = (4/3) * pi * r^3 = (4/3) * pi * 3^3 = 36 * pi. Volume of wire (cylinder) = pi * r_w^2 * h. Radius of wire = 0.1 cm. So, 36 * pi = pi * (0.1)^2 * h. 36 = 0.01 * h, so h = 3600 cm. Converting to meters, h = 36 m.

AI explanation

By the volume conservation method, the volume of the copper sphere equals the volume of the cylindrical wire, giving (4/3) * pi * 3^3 = pi * (0.1)^2 * h. Solving for h gives h = 36 / (0.01) = 3600 centimeters. Converting this length to metres gives a wire length of 36 metres.

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