Question

a hemispherical bowl with radius 6cm is filled with water.if the water is tranferred into cylindrical vessel of base radius 3cm, find the height to which water rises in cylindrical vessel. ( use pie= 22/7 )

Answer 1

$$\begin{gathered} \mathrm{Given} \\ \mathrm{Radius}\mathrm{of}\mathrm{hemispeherical}\mathrm{bowl}=6\mathrm{cm} \\ \mathrm{Volume}\mathrm{of}\mathrm{hemipeherical}\mathrm{bowl}=\frac{2}{3}{\mathrm{\pi r}}^3 \\ \Rightarrow \frac{2}{3}\times \mathrm{\pi }\times 6^3 \\ \mathrm{Radius}\mathrm{of}\mathrm{cylindrical}\mathrm{vessel}=3\mathrm{cm} \\ \mathrm{Let}\text{'}\mathrm{h}\text{'}\mathrm{be}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{vessel} \\ \mathrm{Volume}\mathrm{of}\mathrm{cylindrcal}\mathrm{vessel}={{\mathrm{\pi r}}_1}^2\mathrm{h} \\ =\mathrm{\pi }\times 3^2\times \mathrm{h} \\ \mathrm{From},\mathrm{the}\mathrm{given}\mathrm{data} \\ \frac{2}{3}\times \mathrm{\pi }\times 6^3=\mathrm{\pi }\times 3^2\times \mathrm{h} \\ \Rightarrow \frac{2}{3}\times 6\times 6\times 6=9\times \mathrm{h} \\ \Rightarrow \mathrm{h}=16\mathrm{cm} \\ \mathrm{Rise}\mathrm{in}\mathrm{water}\mathrm{level}\mathrm{in}\mathrm{cylindrical}\mathrm{vessel}=16\mathrm{cm} \end{gathered}$$