Geometry
posted by aubrie .
what are the dimensions of two cylinders where the first cylinder has a greater surface area and the second cylinder has a greater volume?

There are an infinite number of possibilities. You need to provide more information, if you want a unique answer.

let the height be h, and the radius be r
Volume = πr^2h
Surface area = 2πr^2 + 2πrh
volume > SA
πr^2h > 2πr^2 + 2πrh, divide by πr
rh > 2r + 2h
rh  2h > 2r
h > 2r/(r2)
if SA > volume
then h < 2r/(r2)
for both to be true,
h = 2r/(r2)