Question

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

Answer 1

Question:

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

Answer:

Volume of cylindrical tank is πr^2h

= πr^2h

= 22/7 × 10/2 × 10/2 × 2

= 1100 / 7 m^3

Radius of pipe = 10 cm = 0.1 m

Speed = 4 km / hour

= 4000m / hr

Let length of water column be 'x' meter

Volume of water column = 1100/7 m^3

= πr^2h

= 22/7 × 0.1 × 0.1 × x

= 0.22x/7

1100/7 = 0.22x/7

1100 = 0.22x

1100/0.22 = x

5000 = x

Length of water column = 5000 m = 5km

Time = Distance / Speed

Time = 5 / 4

Time = 1.25 hrs

Time = 1 hours and 15 minutes

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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

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

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