Given area three cylindrical bukets X,Y.Z whose circular bases are of radii 1,2,3 units ,respectively . Intially Water is filled in these bukets upto the same water transferred from Z to X so that they both have the same volume of water Some water is then transferred between X and y so that they both have same volume of water if `h_(z)` denote the heights of water at this stage in the bukets y, z, respectively , then the ratio `(h_(y))/(h_(z))` equals -

Options

A. `(4)/(9)`
B. 1
C. `(9) /(4)`
D. `(81)/(40)`

Answer

D

Explanation

intitally ` V_(1) = pi H,V_(2) =4pi H,V_(3) =piH`
`step -1 : V_(1) =5piH,V_(2) = 4pi H,V_(3) =5pi H`
`step -2 ,V_(1) =4.5piH, V_(2) = 4.5 pi H, V_(3) =5pi H `
`" Hence " pi 2^(2) ,h_(y) =4.5pi H`
`pi 3^(2) h_(z)= 5pi H`
`implies (4h_(y) )/(9h_(z))=(4.5)/(5) =. (4h_(y) )/(9h_(z) ) =(81)/(40)`