Question

A farmer connects a pipe of internal diametre 20 cm from a canal into a cylindrical tank which is 10 m in diameter

Answer 1

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Answer 2

Correct question →

A farmer connects a pipe of internal diameter of 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep .If water flows through the pipe at the rate of 4 km /hr ,In how much time will tank be filled completely ?

Solution →

Water flows at the rate of 4km /hr in pipe

--→ Water flows 4000m in 1hr in pipe of diameter 20cm

$\tt VOLUME_{cylindrical\:pipe} = \pi r^2 h \\\tt VOLUME_{cylindrical\:pipe} = \pi \dfrac{10}{100} 4000 m^3 \\\\\tt VOLUME_{cylindrical\:pipe} = \pi 40m\: -(1)$

Now, Diameter of cylindrical tank = 10m

Radius of cylindrical tank = 5m

Height of cylindrical tank= 2m

$\tt VOLUME_{cylindrical\:tank} = \pi r^2 h \\\tt VOLUME_{cylindrical\:pipe} = \pi 5\times5\times2 \\\tt VOLUME_{cylindrical\:pipe} = \pi 50 m^3-(2)$

$\bigstar \sf Time \:taken\:to \:fill \:tank = \dfrac{ VOLUME_{cylindrical\:pipe} }{VOLUME_{cylindrical\:pipe} }$

$\bigstar \sf Time \:taken\:to \:fill \:tank = \dfrac{50\pi }{40 \pi }$

Total time taken= 5/4hrs or 1  hr 15 minutes.

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