• # 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 $2\text{ }cm$.

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