Multiple choice

Water flows in a tank $150$ m $\times 100$ m at the base, through a pipe whose cross-section is $2$ dm by $1.5$ dm at a speed of $15$km per hour. In what time, will the water be $3$ metres deep?

  1. $50$ hours
  2. $150$ hours
  3. $100$ hours
  4. $200$ hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of water needed = 150 * 100 * 3 = 45000 m^3. Pipe cross-section = 2 dm * 1.5 dm = 0.2 m * 0.15 m = 0.03 m^2. Speed = 15 km/h = 15000 m/h. Volume per hour = 0.03 * 15000 = 450 m^3/h. Time = 45000 / 450 = 100 hours.

AI explanation

Using the volume equivalence formula, the required volume is the base area of one hundred fifty meters multiplied by one hundred meters and a depth of three meters, equalling forty-five thousand cubic meters. The pipe cross-section is two dm by one point five dm, converting to zero point two meters by zero point one five meters, which is an area of zero point zero three square meters. The water flows at fifteen kilometers per hour, which converts to fifteen thousand meters per hour, yielding a flow rate of zero point zero three multiplied by fifteen thousand, which is four hundred fifty cubic meters per hour. Dividing the total required volume of forty-five thousand cubic meters by the hourly flow rate of four hundred fifty gives a total time of one hundred hours.

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