• # question_answer A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by  $\frac{32}{9}cm$. Find the diameter of the cylindrical vessel.

 Given, diameter of sphere $=12\text{ }cm$ then, radius of sphere $(r)=\frac{12}{2}=6\,cm$ Volume of sphere $=\frac{4}{3}\pi {{r}^{3}}$ $=\frac{4}{3}\times \pi \times {{(6)}^{3}}c{{m}^{3}}$ Now, sphere is completely submerged in water and rise in water in cylindrical vessel is $3\frac{5}{9}cm.$ Volume of sphere = Volume of cylindrical vessel. $\frac{4}{3}\pi \times {{(6)}^{3}}=\pi {{r}^{2}}\times \frac{32}{9}$ ${{r}^{2}}=\frac{4\times 6\times 6\times 6\times 9}{3\times 32}$ $r=\sqrt{81}$ $r=9\,\,cm$ $\therefore$ Diameter of the cylindrical vessel is $18\text{ }cm$.

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