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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 ├Ч ╧А ├Ч r┬▓ ├Ч h = 1/3 ├Ч ╧А ├Ч (6)┬▓ ├Ч 8 = 96╧А Volume of one sphere = 4/3 ├Ч ╧А ├Ч r┬│ = 4/3 ├Ч ╧А ├Ч (2)┬│ = 32/3 ╧А Number of spheres = Volume of cone / Volume of sphere = 96╧А / (32/3 ╧А) = 9 Correct answer: b. 9

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