a conical vessel whose internal radius is 5 cm and height 24 cm full of water.the water is emptied into a cylinderical vessel with internal radius 10 cm. find the height to which water rises?

Height = 24 cm

Since the conical vessel is full of water, so volume of water = volume of vessel

So, volume of water = $\frac{1}{3}{\mathrm{\pi r}}^{2}\mathrm{h}=\frac{1}{3}\times \frac{22}{7}\times {5}^{2}\times 24=\frac{4400}{7}{\mathrm{cm}}^{3}$

Now, this volume of water is emptied in a cylindrical vessel.

So, suppose the height of level of water in the cylindrical vessel is

*h*.

and radius of base of cylindrical vessel = 10 cm

So, volume of water in cylindrical vessel up to height

*h*= $\mathrm{\pi}\times {10}^{2}\times \mathrm{h}=\frac{4400}{7}{\mathrm{cm}}^{3}$

$\Rightarrow \frac{22}{7}\times 100\times h=\frac{4400}{7}\phantom{\rule{0ex}{0ex}}\Rightarrow h=\frac{4400}{22\times 100}=2$

Therefore, height of water level in cylindrical vessel = 2 cm

**
**