Multiple choice

Through a cylindrical pipe of internal radius $7cm$, water flows out at the rate of $5cm/sec$. Calculate the volume of water (in litres) discharged through pipe in half an hour.

  1. $1386$ litres
  2. $186$ litres
  3. $136$ litres

  4. None of these
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A Correct answer
Explanation

Volume = cross-sectional area * flow rate * time. Area = pi * r^2 = 22/7 * 7 * 7 = 154 cm^2. Flow rate = 5 cm/sec. Time = 30 min = 1800 sec. Volume = 154 * 5 * 1800 = 1,386,000 cm^3. Since 1000 cm^3 = 1 litre, volume = 1386 litres.

AI explanation

The cross-sectional area of the pipe is pi * r^2, which is 22/7 * 7 * 7 = 154 cm^2. The length of the water column in half an hour is the flow rate multiplied by time, giving 5 cm/sec * 1800 sec = 9000 cm. The volume of water discharged is 154 * 9000 = 1386000 cm^3, and converting to liters gives 1386000 / 1000 = 1386 liters.

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