Question

# A farmer connects a pipe of internal diameter $20\mathrm{cm}$ form a canal into a cylindrical tank in her field, which is $10\mathrm{m}$ in diameter and $2\mathrm{m}$ deep. If water flows through the pipe at the rate of $3\mathrm{km}/\mathrm{hr}$, in how much time will the tank be filled?

Open in App
Solution

## Step 1:Finding out the volume of water flowing and that of cylindrical tank.Radius of Cylindrical tank $\left(\mathrm{r}\right)=5\mathrm{m}=500\mathrm{cm}\left[\mathrm{Since}\mathrm{radius}=\frac{\mathrm{diameter}}{2},1\mathrm{m}=100\mathrm{cm}\right]$Depth of Cylindrical tank $\left(\mathrm{h}\right)=2\mathrm{m}=200\mathrm{cm}$Speed of water flows in pipe $=3\mathrm{km}/\mathrm{hr}=\left(3,000\mathrm{m}/\mathrm{hr}\right)\left[\because 1\mathrm{km}=1000\mathrm{m}\right]$Volume of water flows in $1\mathrm{hr}={\mathrm{\pi r}}^{2}\mathrm{h}=\mathrm{\pi }×10×10×300000{\mathrm{cm}}^{3}$Volume of cylindrical tank $={\mathrm{\pi r}}^{2}\mathrm{h}=\mathrm{\pi }×500×500×200{\mathrm{cm}}^{3}$Step 2 : Finding the time taken to fill the tank.$\mathrm{Time}\mathrm{taken}\mathrm{to}\mathrm{fill}\mathrm{the}\mathrm{tank}=\mathrm{Volume}\mathrm{of}\mathrm{cylindrical}\mathrm{tank}÷\mathrm{Volume}\mathrm{of}\mathrm{water}\mathrm{flow}\mathrm{in}1\mathrm{hr}$$⇒\mathrm{t}×\left(30\mathrm{\pi }\right)={\mathrm{\pi r}}^{2}\mathrm{h}\phantom{\rule{0ex}{0ex}}⇒\mathrm{t}×\left(30\mathrm{\pi }\right)=\mathrm{\pi }×{5}^{2}×2\phantom{\rule{0ex}{0ex}}⇒\mathrm{t}=\frac{5\mathrm{x}5\mathrm{x}2}{30}\phantom{\rule{0ex}{0ex}}⇒\mathrm{t}=\frac{5}{3}\mathrm{hours}\phantom{\rule{0ex}{0ex}}⇒\mathrm{t}=\frac{5}{3}×60\mathrm{mins}\left[\mathrm{Since}1\mathrm{hr}=60\mathrm{mins}\right]\phantom{\rule{0ex}{0ex}}⇒\mathrm{t}=100\mathrm{minutes}\phantom{\rule{0ex}{0ex}}⇒\mathrm{t}=1\mathrm{hour}40\mathrm{minutes}$Hence, The time required to fill the tank is $1\mathrm{hour}40\mathrm{minutes}$.

Suggest Corrections
0
Explore more