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.