Multiple choice

A solid sphere of radius $x$ cm is melted and cast into a shape of a solid cone of radius $x$ cm. The height of the cone is:

  1. $3x$ cm
  2. $x$ cm
  3. $4x$ cm
  4. $2x$ cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of sphere = (4/3) * pi * x^3. Volume of cone = (1/3) * pi * r^2 * h. Given r = x, (4/3) * pi * x^3 = (1/3) * pi * x^2 * h. Simplifying gives 4x = h.

AI explanation

Because the solid sphere is melted and recast into a solid cone, their volumes must be equal. Setting (4/3)πx^3 equal to (1/3)πx^2h gives 4x^3 = x^2h. Solving for h yields h = 4x. The result is 4x cm.

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