A right circular cylindrical tank of radius ‘r’ cm and height ‘r+12’ cm…
2022
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’ number of hemispherical bowls such that each bowl is filled up to its maximum capacity. If the maximum capacity of each bowl is 11r³/35 cm³, which among the following (I, II, III & IV) is/are the possible value/s of ‘N’. (R & N are positive integers)
I. 6
II. 34
III. 25
IV. 19
- A.
Both I & II
- B.
Both III & IV
- C.
Both I & III
- D.
Both II & III
- E.
None of these
Show answer & explanation
Correct answer: D
Cylinder volume = pi r^2(r + 12). Using pi = 22/7, this is (22/7)r^2(r + 12).
Each hemispherical bowl has capacity 11r^3/35.
N = [(22/7)r^2(r + 12)] / [11r^3/35] = 10(r + 12)/r = 10 + 120/r.
Since r and N are positive integers, N is possible when r divides 120.
N = 34 gives r = 5, and N = 25 gives r = 8. N = 6 is impossible because N must be greater than 10, and N = 19 gives r = 120/9, not an integer.
Therefore the possible values are II and III.