Two similar cylinders have a scale factor of 1.6/3. find the ratio of their volumes.

So assuming that each thing is 1.6:3 smaller
radius=1.6r   to   radius=3r
height=1.6h   to   height=3h

volume=pi times r^2 times height

1.6                                                           3
pi times (1.6r)^2 times 1.6h    to         pi times (3r)^2 times 3h
pi times 2.56r^2 times 1.6h      to       pi times 9r^2 times 3h
 pi times 4.096hr^2              to      pi times 27hr^2

so the ratio is
pi times 4.096hr^2:pi times 27hr^2
divide both sides by pi
4.096hr^2:27hr^2
divide both sides by hr^2
4.096:27

answer is 4.096/27