question_answer

A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. (Use \[\pi =\frac{22}{7}\])

Answer:

Given, radius (r) and height (h) of conical vessel is 5 cm and 24 cm respectively.

Volume of water in conical vessel \[=\frac{1}{3}\pi {{r}^{2}}h\]

\[=\frac{1}{3}\times \frac{22}{7}\times 5\times 5\times 24\]

\[=\frac{13200}{21}c{{m}^{3}}\]

Since water is emptied into a cylindrical vessel.

\[\because \] Volume of water in conical vessel = Volume of water in cylindrical vessel

\[\frac{13200}{21}=\pi {{R}^{2}}H\]

\[\frac{13200}{21}=\frac{22}{7}\times 10\times 10\times H\]

\[H=\frac{13200\times 7}{21\times 22\times 10\times 10}\]

\[H=2\,cm\]

\[\therefore \] Height of water rise in cylindrical vessel is \[2\text{ }cm\].