Multiple choice

A metallic solid of volume $3,600 mm^{3}$ melted and drawn into the form of a wire of height $12$ mm. Find the radius of the wire. (Use $\pi = 3$)

  1. $12$ mm
  2. $11$ mm
  3. $10$ mm
  4. $14$ mm
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C Correct answer
Explanation

Volume of wire = pi * r^2 * h. 3600 = 3 * r^2 * 12. 3600 = 36 * r^2. r^2 = 100. r = 10.

AI explanation

The volume of the metallic solid is 3600 cubic mm, which becomes the volume of the wire that is formed, having a height of 12 mm. Using the cylinder volume formula V equals pi times radius squared times height, we set 3600 equal to 3 times radius squared times 12. Solving for the radius squared gives 3600 divided by 36, which equals 100, so the radius is the square root of 100. The radius of the wire is 10 mm.

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