Question 717051
The volume of a cylinder is calculated as the surface area of its base times the height.
 
CORRECTED CORRECTION:
This is what happens when you reach retirement age.
If the radius {{{R}}} of one cylinder is 5 times the diameter of the other,
Then {{{R=5*(2r)}}} --> {{{R=10r}}}
and the ratio of volumes will be {{{10^2=highlight(100)}}}
  
OOPS! It was not 2 times! My previous solution below is the answer to the problem in my head, as I (mis)remembered it, not the answer to the problem as written above.
The two cylinders have height {{{h}}} and radii {{{r}}} and {{{2r}}} (in the dictionary, the word radiuses is allowed as a plural, but spellchecker does not like it).
Their volumes will be
{{{pi*r^2*h}}} and {{{pi*(2r)^2*h=pi*4r^2*h}}}
so the ratio of their volumes is
{{{pi*4r^2*h/(pi*r^2*h)=highlight(4)}}} or 4:1 if you prefer to express it that way.
The larger cylinder has a volume that is 4 times the volume of the smaller one.