The volume of a cylinder is given by
[tex]V = \pi hr^2[/tex]
Let [tex]h\mapsto 2h[/tex] and [tex]r\mapsto 2r[/tex]
The new volume becomes
[tex]V = \pi(2h)(2r)^2 = \pi\cdot 2h \cdot 4r^2 = 8\pi hr^2 [/tex]
So, the new volume is 8 times the original volume. In fact, volume scales linearly with the height and quadratically with the radius.
