Question

Given are three cylindrical buckets X, Y, Z whose circular bases are of radii 1, 2, 3 units, respectively, Initially, water is filled in these buckets up to the same height. Some water is then 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 the same volume of water. If h${}_y$, h${}_z$ denote the heights of water at this stage in the buckets Y,Z, respectively, then the ratio $\frac{h_y}{h_z}$ equals.

• A. $\frac{4}{9}$
• B. 1
• C. $\frac{9}{4}$
• D. $\frac{81}{40}$

Answer 1

The correct option is D

$\frac{81}{40}$

V = $\pi$h $\pi$4h $\pi$9h $\dots$.. stage (1)
$\pi$h 4$\pi$h 5$\pi$h $\dots$.. stage (2)
4.5$\pi$h 5.4$\pi$h 5$\pi$h $\dots$.. stage (3)
$4\pi .h_y=\frac{9\pi h}{2}$
$9\pi h_z=5\pi h$
$h_y=\frac{9h}{8}$
$h_z=\frac{5}{9}h$
$\frac{h_y}{h_z}=\frac{9h}{8}/\frac{5}{9}h$
$=\frac{81}{40}$