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    Question

    A right circular cylindrical tank of radius 'R' meter

    and height 'R + 7' meter contains oil. The entire quantity of oil is taken out from the cylindrical tank and poured into 'N' number of hemispherical bowls such that each bowl is filled up to their maximum capacity. If the maximum capacity of each bowl is 11R3/42 m3. Which among the following (i, ii, iii and iv ) is/are the possible values of 'N'. (R and N are positive integers). i. 13 ii. 8 iii. 16 iv. 17
    A Only i Correct Answer Incorrect Answer
    B Only ii and iv Correct Answer Incorrect Answer
    C None of these Correct Answer Incorrect Answer
    D Only ii Correct Answer Incorrect Answer
    E Only i and iii Correct Answer Incorrect Answer

    Solution

    When we pour oil from cylindrical tank to hemispherical bowls, the volume remains constant. So, volume of cylindrical tank = volume of hemispherical bowls Ļ€R2 (R + 7) = N x 11R3/42 12R + 84 = NR N = 12 + 84/R From i: Take N = 13 13 = 12 + 84/R R = 84 i can be possible. From ii Take N = 8 8 = 12 + 84/R R = -21 ii cannot be possible. From iii Take N = 16 19 = 12 + 84/R R = 12 iii can be possible. From iv: Take R = 17 17 = 12 + 84/R R = 16.8 iv cannot be possible. So, only i and iii follows

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