Question 970702
 Two similar cylinders have volumes of 120 in cubed and 405 in cubed. 
How do I use the scale factor and volume to compute the ratio of their heights?
:
{{{(pi*r1^2*h1)/(pi*r2^2*h2)}}} = {{{120/405}}}
Cancel out pi, reduce the ratio fraction
{{{(r1^2*h1)/(r2^2*h2)}}} = {{{8/27}}}
note that both the denominator and numerator at perfect cubes
How convenient to make r1=2, h1=2 and r2=3, h2=3
{{{(2^2*2)/(3^2*3)}}} = {{{8/27}}}
we can see the height ratio = 2:3