Multiple choice

Water in a cylindrical tank of a diameter $4m$ and height $10m$ is released through a cylindrical pipe of diameter $10cm$ at the rate of $2.5Km/hr$. How much time will it take to empty the half of the tank? Assume that the tank is full of water to begin with.

  1. $3hr$ $12min$
  2. $2hr$ $12min$
  3. $3hr$ $22min$

  4. None of these
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A Correct answer
Explanation

Volume of tank = pi * r^2 * h = pi * 2^2 * 10 = 40pi. Half volume = 20pi m^3. Pipe flow rate = Area * velocity = pi * (0.05)^2 * 2500 m/hr = pi * 0.0025 * 2500 = 6.25pi m^3/hr. Time = 20pi / 6.25pi = 3.2 hours. 0.2 hours = 12 minutes. Total = 3 hours 12 minutes.

AI explanation

Using the formula for the volume of a cylinder, the volume of half the tank is pi times the radius squared times the height, yielding pi times 2 squared times 5, which is 20 pi cubic metres. The cross-sectional area of the pipe is pi times 0.05 squared, equaling 0.0025 pi square metres. The flow rate is this area multiplied by the velocity of 2500 m/hr, giving 6.25 pi cubic metres per hour. The time required to empty half the tank is the volume of 20 pi divided by 6.25 pi, which equals 3.2 hours, or 3 hours and 12 minutes.

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