Answer:
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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