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    Question

    A sphere of radius 21 cm is melted and recast into 66

    smaller spheres of equal size. Find the radius of each smaller sphere(approximately).
    A 7 cm Correct Answer Incorrect Answer
    B 9 cm Correct Answer Incorrect Answer
    C 5 cm Correct Answer Incorrect Answer
    D 4 cm Correct Answer Incorrect Answer

    Solution

    Volume of a sphere = (4/3)πr³. Volume of the large sphere = (4/3)π(21)³ = (4/3)π × 9261 = 12348π cm³. Volume of one smaller sphere = Total volume ÷ Number of smaller spheres = 12348π ÷ 66 = 187π cm³. Let the radius of each smaller sphere be r. (4/3)πr³ = 187π. r³ = (187 × 3)/4 = 140.25. r = ∛140.25 ≈ 5 cm. Correct answer: c) 5 cm

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