Question 879877
The smaller cylinder:
{{{A=highlight_green(2pi*r^2+h2pi*r=220)}}} and {{{V=highlight_green(h*pi*r^2=314)}}}.


Using volume equation, {{{h=314/(pi*r^2)}}}; substitute into the area equation:
{{{2pi*r^2+(314/(pi*r^2))2pi*r=314}}}
{{{2pi*r^2+628/r=314}}}
{{{2pi*r^3+628=314r}}}
{{{2pi*r^3-314r+628=0}}}
{{{highlight(pi*r^3-157r+314=0)}}}---Obviously not yet finished, but a graphing calculator might help in getting a value for r, the diameter for the small cylinder; and from this, the length of the cylinder can be found.  The ratio between the two cylinders can then be used.


(Roots appear near 2.20 and 5.70; evaluate each carefully and judge if useful).