Multiple choice

A child reshapes a cone made up of clay of height $24\ cm$ and radius $6\ cm$ into a sphere. The radius (in $cm$) of the sphere is

  1. $6$
  2. $12$
  3. $24$
  4. $48$
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A Correct answer
Explanation

Volume of cone = (1/3)*pi*r^2*h = (1/3)*pi*6^2*24 = 288*pi. Volume of sphere = (4/3)*pi*R^3. Setting them equal: 288*pi = (4/3)*pi*R^3 -> 216 = R^3 -> R = 6.

AI explanation

When the cone is reshaped into a sphere, the volume remains constant, meaning the volume of the cone equals the volume of the sphere. Using the formulas, (1/3) * pi * r^2 * h = (4/3) * pi * R^3, where r is the cone's radius, h is the cone's height and R is the sphere's radius. Substituting the given values, (1/3) * pi * 6^2 * 24 = (4/3) * pi * R^3, which simplifies to 864 = 4 * R^3, giving R^3 = 216 and R = 6 cm. The radius of the sphere is 6 cm.

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