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A right circular cylindrical tank of radius \(r\) cm and height \(r+12\) cm contains milk. The entire quantity of milk is taken out from the cylindrical tank and poured into \(N\) hemispherical bowls such that each bowl is filled to its maximum capacity. The maximum capacity of each bowl is \(\frac{11\pi^3}{35}\) cm\(^3\). Which among the following values of \(N\) are possible? (\(r\) and \(N\) are positive integers) I. 6 II. 34 III. 25 IV. 19
- Both I & II
- Both III & IV
- Both I & III
- Both II & III
- None of these
Correct answer: None of these
Solution
The cylinder volume is \(\pi r^2(r+12)\), and it must equal \(N\times \frac{11\pi^3}{35}\). This gives a constraint on integer \(r\) and \(N\), and none of the listed values satisfy it.
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