Question

    A sphere is melted and recast into 64 smaller spheres of

    equal size. If the radius of the original sphere is 16 cm, find the radius of each smaller sphere.
    A 2 cm Correct Answer Incorrect Answer
    B 4 cm Correct Answer Incorrect Answer
    C 6 cm Correct Answer Incorrect Answer
    D 8 cm Correct Answer Incorrect Answer

    Solution

    Volume of the original sphere = (4/3)╧АR┬│, where R = 16 cm. Volume of each smaller sphere = (4/3)╧Аr┬│, where r is the radius of the smaller sphere. Since the original sphere is recast into 64 smaller spheres: (4/3)╧А(16┬│) = 64 ├Ч (4/3)╧Аr┬│. Cancel (4/3)╧А on both sides: 16┬│ = 64 ├Ч r┬│. Simplify: r┬│ = 16┬│/64 = 16┬▓/4 = 64. r = 4 cm. Correct answer: b. 4 cm

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