Multiple choice

If a cubical metal of dimensions 44 cm $\times$ 30 cm $\times$ 15 cm was melted and cast into a cylinder of height of 28 cm, then what is its radius?

  1. $15$
  2. $15\sqrt 3$
  3. $3\sqrt 6$
  4. $5\sqrt 3$
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A Correct answer
Explanation

Volume of cuboid = 44 * 30 * 15 = 19800. Volume of cylinder = pi * r^2 * h = 22/7 * r^2 * 28 = 88 * r^2. Equating: 88 * r^2 = 19800. r^2 = 19800 / 88 = 225. r = 15.

AI explanation

When the cuboidal metal is melted, its volume of 44 * 30 * 15 = 19800 cubic cm is conserved and equals the volume of the cylinder. Using the cylinder volume formula V = pi * r^2 * h with a height of 28 cm gives pi * r^2 * 28 = 19800. This gives r^2 = 225, and taking the square root gives the radius as 15 cm.

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