Multiple choice

The water in a rectangular reservoir having a base $80 m$ by $60m$ is $6.5 m$ deep. In what time can the water be emptied by a pipe of a square cross-section is of side $20 cm$, if the water runs through the pipe at the rate of $15 km$ per hours?

  1. $26$ hours
  2. $42$ hours
  3. $52$ hours
  4. $65$ hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of water = 80 * 60 * 6.5 = 31200 cubic meters. Pipe cross-section = 0.2m * 0.2m = 0.04 sq meters. Speed = 15000 m/h. Volume per hour = 0.04 * 15000 = 600 cubic meters. Time = 31200 / 600 = 52 hours.

AI explanation

Using the volume flow rate formula, we first find the volume of the reservoir as length times width times depth, giving 80 m times 60 m times 6.5 m equals 31200 cubic meters. The water flows through the square pipe at 15 km per hour, which is 15000 m, with a cross-sectional area of 0.2 m times 0.2 m equals 0.04 square meters; this gives a flow rate of 15000 times 0.04 equals 600 cubic meters per hour. Dividing the total volume by the flow rate gives 31200 divided by 600, which equals 52 hours.

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