Multiple choice

Water flows out through a circular pipe whose internal diameter is $2 cm$, at the rate of $6$ metres per second into a cylindrical tank. The radius of whose base is $60 cm$. The rise in the level of water in $30$ minutes is

  1. $3 m$
  2. $-3 m$
  3. $6 m$
  4. $-6 m$
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A Correct answer
AI explanation

Using the volume flow continuity method, the total volume of water flowing into the cylindrical tank over 30 minutes is calculated by multiplying the pipe's cross-sectional area by the flow rate and the time. The pipe's cross-sectional area is pi multiplied by 0.01 m squared and the flow rate is 6 m per second, so over 1800 seconds the volume equals 1.08 pi cubic meters. This volume is distributed across the base of the cylindrical tank, so the rise in water level is the water volume divided by the base area of pi multiplied by 0.6 m squared. Canceling pi and calculating 1.08 divided by 0.36 gives a rise in the water level of 3 m.

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