Multiple choice

A cone of height $24$ cm and radius of base $6$ cm is made up of modelling clay. A child reshapes it in the form of a sphere. The radius of sphere is

  1. $1$ cm
  2. $2$ cm
  3. $4$ cm
  4. $6$ cm
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D Correct answer
Explanation

The volume of the cone is (1/3) * pi * r^2 * h = (1/3) * pi * 6^2 * 24 = 288 * pi. The volume of the sphere is (4/3) * pi * R^3. Setting them equal: (4/3) * pi * R^3 = 288 * pi, which gives R^3 = 216, so R = 6.

AI explanation

Because the volume remains constant during the reshaping, the volume of the cone equals the volume of the sphere. Using the formulas 1/3 * pi * r^2 * h and 4/3 * pi * R^3, we set 1/3 * pi * 6^2 * 24 equal to 4/3 * pi * R^3. This simplifies to 36 * 24 = 4 * R^3, so R^3 = 216, meaning the radius of the sphere is 6 cm.

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