Multiple choice

A cuboidal metal of dimensions $44cm\times 30cm\times 15cm$ was melted and case into a cylinder of height $28cm$. Its radius is

  1. $20cm$
  2. $15cm$
  3. $10cm$

  4. None
Reveal answer Fill a bubble to check yourself
B 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. Setting 88 * r^2 = 19800 gives r^2 = 225, so r = 15.

AI explanation

First, find the total volume of the cuboid using the formula length times width times height, which gives 44 * 30 * 15 to equal 19800 cubic cm. Since the volume remains constant when melted and recast into a cylinder, we set the cylinder volume formula, pi * r^2 * h, equal to 19800. Using a height of 28 cm and pi as 22/7, the equation becomes (22/7) * r^2 * 28 = 19800. Solving this yields 88 * r^2 = 19800, so r^2 = 225, meaning the radius is 15 cm.

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