Question

34. A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in
her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate
of 3 km/h, in how much time will the tank be filled?​

Answer 1

$\red{ \frak {Given}}\begin{cases} \sf{Internal\:diameter\:of\:a\:pipe\:= \frak{20\:cm}} \\ \\ \sf{Radius\:of\:Pipe\:=\:10\:cm\:= \frak{\dfrac{1}{10}}\:\frak m} \\ \\\sf{Diameter\:of\:cylindrical\:tank\:= \frak{10\:m}\:;\:r\:=\frak{5\:m}} \\ \\\sf{Depth\:of\:cylindrical\:tank\:= \frak{2\:m}}\\ \\ \sf{Speed\:of\:water\:=\frak{3\:km/hr}}\end {cases}$

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Need to find : Time required to fill the water tank.

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We Know,

• Speed of Water is 3 km/hr.

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$\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{\dfrac{3000}{60}}\:m/minute$

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$\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{50\:m/minute }$

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Let time required to fill the tank be n' minutes.

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• Flowing water in 'n' minutes = Volume of water tank

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$\:\::\:\Longrightarrow\sf\:{\pi\:\times{ \bigg(\dfrac{1}{2} \bigg)}^{2}\:\times\:(n\:\times\:50)\:=\:\pi\:\times\:(5)^{2} }\:{\times\:2 }$

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$\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{\dfrac{1}{100}}\:n\:\times\:50\:=\:50$

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$\:\:\:\:\:\:\::\:\Longrightarrow\:{\underline{\boxed{\frak{\pink{n\:=\:100\:minutes }}}}}\:\bigstar$

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$\:\therefore\:{\underline{\sf{Time\:required\:to\:fill\:the\:water\:tank\:is\:{\textsf{\textbf{100\:minutes}}}}}}.$

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