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    Question

    A solid metallic cylinder of radius 5 cm and height 8 cm

    is melted and recast into 10 identical solid cones, each having radius 2 cm. What is the height of each cone?
    A 15 cm Correct Answer Incorrect Answer
    B 33 cm Correct Answer Incorrect Answer
    C 20 cm Correct Answer Incorrect Answer
    D 12 cm Correct Answer Incorrect Answer

    Solution

    ATQ, Volume of cylinder = ╧Аr┬▓h = ╧А ├Ч 5┬▓ ├Ч 8 = 200╧А. Volume of one cone = (1/3)╧АR┬▓H = (1/3)╧А ├Ч 2┬▓ ├Ч H = (4/3)╧АH. For 10 cones: total volume = 10 ├Ч (4/3)╧АH = (40/3)╧АH. Equating: 200╧А = (40/3)╧АH => 200 = (40/3)H => H = 200 ├Ч 3 / 40 = 15 cm.

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