Multiple choice

A rectangular water-tank measuring $\displaystyle 80\ cm\times 60\ cm\times 60\ cm$ is filled from a pipe of cross-sectional area 1.5 $\displaystyle cm^{2},$ the water emerging at 3.2 m/s. How long does it take to fill the tank?

  1. 10 minutes

  2. 15 minutes

  3. 13 minutes

  4. 12 minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Tank volume = 80 * 60 * 60 = 288000 cm^3. Pipe flow rate = Area * velocity = 1.5 cm^2 * 320 cm/s = 480 cm^3/s. Time = 288000 / 480 = 600 seconds = 10 minutes.

AI explanation

The total volume of the rectangular tank is calculated by multiplying its dimensions, giving 80 cm multiplied by 60 cm multiplied by 60 cm for a total of 288000 cubic centimeters. The rate at which water enters the tank is found by multiplying the pipe's cross-sectional area by the water velocity, which is 1.5 square centimeters multiplied by 320 centimeters per second to get a flow rate of 480 cubic centimeters per second. The time required to fill the tank is the total volume divided by this flow rate, yielding 288000 divided by 480, resulting in 600 seconds. Converting this time into minutes gives 10 minutes.

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