Question

A right circular cone of diameter r cm and height 12 cm rests on the base of right circular cylinder of radius r cm.Their bases are in the same plane and the cylinder is filled with water up to a height of 12 cm.If the cone is then removed,find the height to which water level will fall.

Answer 1

Volume of cone = $\frac{1}{3}\times 12=\pi r^2.cc$
Actual amount of water = Volume of cylinder - Volume of cone
$=12\pi r^2-\pi r^2=11\pi r^2$
Hence when cone is removed, the entire quantity of water occupies space in cylinder. As the entire quantity of water = $11\pi r^2$, the height to which cylinder is filled is 11 cm.
So, water level will fall from 12 cm to 11 cm = 1 cm fall.