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    Question

    A cone has a base radius of 6 cm and a height of 8 cm.

    If it is melted and recast into spheres of radius 2 cm, how many such spheres can be made?
    A 8 Correct Answer Incorrect Answer
    B 9 Correct Answer Incorrect Answer
    C 10 Correct Answer Incorrect Answer
    D 12 Correct Answer Incorrect Answer

    Solution

    Volume of cone = 1/3 × π × r² × h = 1/3 × π × (6)² × 8 = 96π Volume of one sphere = 4/3 × π × r³ = 4/3 × π × (2)³ = 32/3 π Number of spheres = Volume of cone / Volume of sphere = 96π / (32/3 π) = 9 Correct answer: b. 9

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