Multiple choice

A right circular cone is 8 cm. high and the radius of the base is 2 cm. The cone is melted and recast in to a sphere. The diameter of the sphere is -

  1. 8 cm.

  2. 6 cm.

  3. 4 cm.

  4. 2 cm.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cone = (1/3)πr²h = (1/3)π(2²)(8) = (32/3)π cm³. When melted and recast, volume remains constant. Volume of sphere = (4/3)πr³. Equating: (4/3)πr³ = (32/3)π, which gives r³ = 8, so r = 2 cm. Therefore diameter = 4 cm.

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