Question

)Water flows out through a circular pipe whose internal diameter is 2cm,at the rate of 6 meters per second into a cylindrical tank,the radius of whole base is 60 cm.By how much will the level of water rise in 30 minutes

Answer 1

Dear student
$$\begin{gathered} \mathrm{Internal}\mathrm{diameter}\mathrm{of}\mathrm{the}\mathrm{pipe}=2\mathrm{cm} \\ \mathrm{Internal}\mathrm{radius}\mathrm{of}\mathrm{pipe}=1\mathrm{cm} \\ \mathrm{Rate}\mathrm{of}\mathrm{water}\mathrm{flow}=6\mathrm{m}/\sec =600\mathrm{cm}/\sec \\ \mathrm{Therefore},\mathrm{Volume}\mathrm{of}\mathrm{water}\mathrm{which}\mathrm{flows}\mathrm{in}1\sec \\ =\mathrm{Base}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{pipe}\times \mathrm{Rate}\mathrm{of}\mathrm{water}\mathrm{flow} \\ =\frac{22}{7}\times 1\times 1\times 600{\mathrm{cm}}^3 \\ =\frac{22\times 600}{7}{\mathrm{cm}}^3 \\ \mathrm{Therefore},\mathrm{Volume}\mathrm{of}\mathrm{water}\mathrm{which}\mathrm{flows}\mathrm{in}30\min \\ =\frac{22\times 600}{7}\times 30\times 60{\mathrm{cm}}^3\left[\mathrm{As}30\min =30\times 60\sec \right] \\ \mathrm{It}\mathrm{is}\mathrm{collected}\mathrm{in}\mathrm{the}\mathrm{cylindrical}\mathrm{tank}\mathrm{of}\mathrm{base}\mathrm{radius}60\mathrm{cm}.\mathrm{Let}\mathrm{rise} \\ \mathrm{in}\mathrm{water}\mathrm{level}\mathrm{be}\mathrm{h}\mathrm{cm}. \\ \therefore \mathrm{Volume}\mathrm{of}\mathrm{watre}\mathrm{added}\mathrm{in}\mathrm{it}=\mathrm{Volume}\mathrm{of}\mathrm{water}\mathrm{which}\mathrm{flows}\mathrm{in}30\min \\ \Rightarrow {\mathrm{\pi r}}^2\mathrm{h}=\frac{22\times 600}{7}\times 30\times 60 \\ \Rightarrow \frac{22}{7}\times 60\times 60\times \mathrm{h}=\frac{22\times 600}{7}\times 30\times 60 \\ \Rightarrow \mathrm{h}=300\mathrm{cm} \\ \Rightarrow \mathrm{h}=3\mathrm{m} \end{gathered}$$
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