Multiple choice

If a solid right circular cone of height $24 cm$ and base radius $6 cm$ is melted and recast in the shape of a sphere, then the radius of the sphere is

  1. $6 cm$
  2. $4 cm$
  3. $8 cm$
  4. $12 cm$
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A Correct answer
Explanation

Volume of cone = 1/3 * pi * r^2 * h = 1/3 * pi * 36 * 24 = 288 * pi. Volume of sphere = 4/3 * pi * R^3. 288 * pi = 4/3 * pi * R^3 => 216 = R^3 => R = 6.

AI explanation

Using the right circular cone volume formula, the initial volume is (1/3)π(6)^2(24), yielding 288π cm^3. When melted and recast into a sphere, the volume remains the same, so (4/3)πr^3 = 288π. Solving for r^3 gives 216, meaning the radius of the sphere is 6 cm.

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