NEAP 2007 Exam 2. Need help

[iliketurtles]

From NEAP 2007 EXAM 2.
Question 2
It is discovered that the cause of the pump breakdown is the use of a hose that is too small.
The radius of the incorrect hose is 8 cm.
The radius of the correct hose is 12 cm.
By using the properties of similarity, calculate the ratio:
             volume of water using the incorrect hose : volume of water using the correct hose

The answer:
Question 2
The volume of water in the pool is directly related to the cross-sectional area of the hose.
An error of k in distance causes an error of k2 in area.
Distance
8 : 12 = 2 : 3

Area
4 : 9

_______________________________________________________________________________

Why are we squaring the "k" value? Surely we would cube it? because the question is making reference to volume....anyone can explain how they got this solution?
Cheers.

[butene]

well it's only necessary to consider the end of the hose since the lengths from back to front is the same
you would only cube it if the length of the hose has also be enlarged
but in this case only the radius has been scaled up

[iliketurtles]

True - thanks hombre.