Multiple choice

It is required to fix a pipe such that water flowing through it at a speed of $7 m$ per minutes fills a tank of capacity $440$ cubic metres in $10$ minutes. The inner radius of the pipe should be:

  1. $\displaystyle \sqrt{2}m$
  2. $2 m$
  3. $\displaystyle \frac{1}{2}m$
  4. $\displaystyle \frac{1}{\sqrt{2}}m$
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A Correct answer
Explanation

Volume = Area * Speed * Time. 440 = (pi * r^2) * 7 * 10. 440 = 70 * pi * r^2. r^2 = 440 / (70 * (22/7)) = 440 / 220 = 2. r = sqrt(2).

AI explanation

The required volume flow rate is the tank capacity divided by the time, which is 440 cubic metres divided by 10 minutes to equal 44 cubic metres per minute. Using the formula for the volume of a cylinder, the cross-sectional area of the pipe multiplied by the flow speed equals the flow rate, so pi times the radius squared times 7 m/min equals 44. Solving for the radius squared gives 44 divided by the product of pi and 7, which simplifies to approximately 2. Therefore, the inner radius of the pipe is the square root of 2 metres.

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