10th Class Mathematics Solved Paper - Mathematics-2016 Outside Delhi Set-I

  • question_answer 17) 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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