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    Question

    A solid right circular cylinder of radius 5 cm and

    height 20 cm is melted and recast into solid spheres of radius 2.5 cm. How many such spheres can be made?
    A 24 Correct Answer Incorrect Answer
    B 18 Correct Answer Incorrect Answer
    C 32 Correct Answer Incorrect Answer
    D 28 Correct Answer Incorrect Answer

    Solution

    Volume of cylinder = ╧Аr┬▓h = ╧А ├Ч 5┬▓ ├Ч 20 = 500╧А cm┬│ Volume of one sphere (r = 2.5 = 5/2): V = (4/3)╧Аr┬│ = (4/3)╧А ├Ч (5/2)┬│ = (4/3)╧А ├Ч 125/8 = (500/24)╧А = (125/6)╧А cm┬│ Number of spheres = 500╧А / [(125/6)╧А] = 500 ├Ч 6 / 125 = 24 So, 24 spheres.

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