Multiple choice

A solid iron cuboidal block of dimensions $4.4\ m \times 2.6\ m\times 1\ m$ is recast into a hollow cylindrical pipe of internal radius $30\ cm$ and thickness $5\ cm$. Find the length of the pipe.

  1. $112\ m$
  2. $110\ m$
  3. $114\ m$
  4. $116\ m$
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A Correct answer
Explanation

Volume of cuboid = 4.4 * 2.6 * 1 = 11.44 m^3. Hollow pipe volume = pi * (R^2 - r^2) * L. Internal radius r = 0.3 m, thickness = 0.05 m, so external radius R = 0.35 m. Volume = pi * (0.35^2 - 0.3^2) * L = pi * (0.1225 - 0.09) * L = pi * 0.0325 * L. 11.44 = (22/7) * 0.0325 * L. Solving for L gives 112 m.

AI explanation

The volume of the cuboidal block is 4.4 times 2.6 times 1, which equals 11.44 m^3. The external radius of the cylindrical pipe is 0.3 m plus 0.05 m, resulting in 0.35 m. Setting the cuboid volume equal to the hollow cylinder volume formula, pi * (0.35^2 - 0.3^2) * length, and solving using pi as 22/7 results in a length of 112 m.

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