Multiple choice

A solid sphere is melted and recast into a right circular cone with a base radius equal to the radius of the sphere. What is the ratio of the height and radius of the cone so formed?

  1. 1 : 2

  2. 4 : 1

  3. 3 : 1

  4. 4 : 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sphere volume = (4/3)πr³. Cone volume = (1/3)πr²h. Since volumes are equal and radii are equal: (4/3)πr³ = (1/3)πr²h. Simplifying: 4r = h, so h : r = 4 : 1.

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