Question

The radius AND height of a cylinder are each doubled. What is the new volume?

Answer 1

The volume of a cylinder is given by

$V = \pi hr^2$

Let $h\mapsto 2h$ and $r\mapsto 2r$

The new volume becomes

$V = \pi(2h)(2r)^2 = \pi\cdot 2h \cdot 4r^2 = 8\pi hr^2$

So, the new volume is 8 times the original volume. In fact, volume scales linearly with the height and quadratically with the radius.