Multiple choice

$12$ sphere of the same size are made from melting a solid cylinder of $16 cm$ diameter and $2 cm$ height. The diameter of each sphere is:

  1. $\sqrt 3 cm$
  2. $2 cm$
  3. $3 cm$
  4. $4 cm$
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D Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * (8)^2 * 2 = 128 * pi. Volume of 12 spheres = 12 * (4/3 * pi * R^3) = 16 * pi * R^3. 16 * pi * R^3 = 128 * pi => R^3 = 8 => R = 2. Diameter = 2 * R = 4 cm.

AI explanation

Using the cylinder volume formula, the original volume is pi*(8^2)2 = 128*pi cubic cm. Let r be the radius of a formed sphere, so the combined volume of 12 spheres is 12(4/3)*pi*r^3 = 16*pi*r^3. Equating the volumes since mass is conserved, 128*pi = 16*pi*r^3, which means r^3 is 8 and r is 2 cm. The diameter is twice the radius, which calculates to 4 cm. The result is 4 cm.

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