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?

Internal radius of conical vessel = 5 cm
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 = $\mathrm{\pi }\times {10}^2\times \mathrm{h} = \frac{4400}{7} {\mathrm{cm}}^3$
$$\begin{gathered} \Rightarrow \frac{22}{7}\times 100\times h = \frac{4400}{7} \\ \Rightarrow h = \frac{4400}{22\times 100} = 2 \end{gathered}$$
Therefore, height of water level in cylindrical vessel = 2 cm