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    Question

    The total surface area of a right circular cone is twice

    the surface area of a sphere having the same radius. If the volume of the sphere is 2304π cm3 , determine the slant height of the cone.
    A 108 cm Correct Answer Incorrect Answer
    B 84 cm Correct Answer Incorrect Answer
    C 96 cm Correct Answer Incorrect Answer
    D 72 cm Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the radius of the sphere and the cone be 'r' cm, and the slant height of the cone be 'l' cm. Total surface area of cone = πrl + πr2 Total surface area of sphere = 4πr2 ATQ; 2 X 4πr2 = πr(l + r) Or, 8r = l + r So, 7r = 'l' Volume of sphere = (4/3) πr3 ATQ; 2304π = (4/3) X π X r3 So, 1728 = r3 So, 'r' = 12 cm So, slant height cone = 7r = 7 x 12 = 84 cm

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