Question

In Fig. 13, a right circular cone of diameter r cm and height 12 cm rests on the base of a right circular cylinder of radius r cm. Their bases are in the same plane and the cylinder is filled with water upto a height of 12 cm. If the cone is then removed, find the height to which water level will fall.

Answer 1

V of the water = V. of the cylinder of height 12 cm
- V of the cone
$=\pi r^{2}h-\frac{1}{3}\pi {\left(\frac{r}{1}\right)}^{2}h$
$=\pi r^2\times 12-\frac{1}{\text{/}3}\times \frac{r^2}{\text{/}4}\times \text{/}1\text{/}2$
$=11\pi r^2$
After removing the cone the water Level will fall
Let it willl fall upto the height h
$\therefore$ V. of the water =$\pi r^2{h}_1$
$\therefore 11\pi r^2=\pi r^2{h}_1$
$\to h_1=11cm$
$\therefore$ The water level will fall upto the height