Question

A farmer connect a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field which is 10m in diameter and 4m deep . If the water flows through the pipe ath the rate of 5km per hour in how much time the tank will be filled.

Answer 1

Answer:

A farmer connect a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field which is 10m in diameter and 4m deep . If the water flows through the pipe ath the rate of 5km per hour in how much time the tank will be filled

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Answer 2

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For the cylindrical pipe : r = 10cm = $\sf{\frac{10}{100}m=\frac{1}{10}m}$

Length of the water that flows through the pipe in 1 hour , h = 3km = 3000m

Volume of water that flows through the pipe in 1 hour = $\sf{\pi {r}^{2} h = \pi \times \frac{1}{10} \times \frac{1}{10} \times 3000 {m}^{2} = 30\pi {m}^{2}}$

For the cylindrical tank : R = 5cm,H = 2cm

Volume of water in the filled tank = $\sf{π{R}^{2}H=π×5×5×2=50π{m}^{2}}$

Time taken to fill the tank with water

= $\sf{ \frac{volume \: of \:water \: in \: the \: filled \: tank }{volume \: of \: water \: that \: flows \: in \: 1 \: hour}}$

= $\sf{ \frac{50\pi}{30\pi} = \frac{5}{3} h = \frac{5}{3} \times 60min . = 100min.}$