Using the proportional relationship, it is found that the radius of the pipe that would allow the sink to drain completely in 14 seconds is of 1.25 cm.
What is a proportional relationship?
A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
[tex]y = kx[/tex]
In which k is the constant of proportionality.
If they are inverse proportional, the relationship is:
[tex]y = \frac{k}{x}[/tex]
In this problem, the amount of time is inversely proportional to the square of the radius of the pipe, hence:
[tex]t = \frac{k}{r^2}[/tex]
A pipe of radius 1 cm can empty a sink in 22 seconds, hence k = 22.
The radius for 14 seconds is:
[tex]t = \frac{k}{r^2}[/tex]
[tex]14 = \frac{22}{r^2}[/tex]
[tex]r^2 = \frac{22}{14}[/tex]
[tex]r = \sqrt{\frac{22}{14}}[/tex]
[tex]r = 1.25[/tex]
The radius of the pipe that would allow the sink to drain completely in 14 seconds is of 1.25 cm.
More can be learned about proportional relationships at https://brainly.com/question/25890103
