Multiple choice

The radius of a solid sphere is $24cm$. It is melted and drawn into a long wire of uniform cross section. Find the length of the wire if its radius is $1.2mm$.

  1. $12.8km$
  2. $128km$
  3. $1.8km$

  4. None of these
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A Correct answer
AI explanation

Because the wire is formed by melting the sphere, their volumes are equal, so (4/3)πR^3 equals the cylindrical volume πr^2h. Substituting the sphere radius of 24 cm and wire radius of 0.12 cm gives (4/3) x 24 x 24 x 24 = 0.12 x 0.12 x h. Solving for h gives a length of 3200000 cm, which equals 12.8 km. The length of the wire is 12.8 km.

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