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    Question

    A right circular cylinder is partially filled with

    water. Two iron spherical balls are completely immersed in the water so that the height of the water in the cylinder rises by 4 cm. If the radius of one ball is half of the other and the diameter of the cylinder is 18 cm, then the radii of the spherical balls are
    A 6 cm and 12 cm Correct Answer Incorrect Answer
    B 4 cm and 8 cm Correct Answer Incorrect Answer
    C 3 cm and 6 cm Correct Answer Incorrect Answer
    D 2 cm and 4 cm Correct Answer Incorrect Answer

    Solution

    Let the radii of the spherical balls be r cm and r/2 cm. The radius of the cylinder R = 18/2 = 9 cm. According to the question (4/3)π [r3 + (r / 2)3] = π R 2 h (4/3) [r3 + (r3) / 8] = 9 × 9 × 4 9r3/8 = 9 x 9 x 3   R3 = 9 × 3 × 8 r = ∛ [3 × 3 × 3 × 2 × 2 × 2] r = 3 × 2 r = 6cm r / 2 = 3cm So, the radii of the cylinder are 3 cm and 6 cm.

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