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. 17Solution
When we pour oil from cylindrical tank to hemispherical bowls, the volume remains constant. So, volume of cylindrical tank = volume of hemispherical bowls ΟR2 (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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