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    Question

    A solid right circular cone of radius 8 cm and height 4

    cm is melted and recast into a solid sphere. What is the radius of the sphere (in cm)?
    A 5 cm Correct Answer Incorrect Answer
    B 3 cm Correct Answer Incorrect Answer
    C 3 cm Correct Answer Incorrect Answer
    D 4 cm Correct Answer Incorrect Answer

    Solution

    ATQ, Volume of cone = (1/3)πr²h = (1/3)π × 8² × 4 = (1/3)π × 64 × 4 = (256/3)π. Volume of sphere = (4/3)πR³. Equate: (4/3)πR³ = (256/3)π ⇒ 4R³ = 256 ⇒ R³ = 64 ⇒ R = 4 cm.

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