Answer
$ \frac{\pi h^3}{48}$
Work Step by Step
The volume V of a cone of radius $r$ and height $h$ is
$V = \frac{1}{3}\pi r^2h$
$tan$ of semi vertical angle of the cone can be written as
$\frac{r}{h} = \frac{4}{16}$
$\Rightarrow r = \frac{h}{4}$
Now, using the volume formula we will get
$V = \frac{1}{3}\pi r^2h = \frac{1}{3}\pi ( \frac{h}{4})^2h = \frac{\pi h^3}{48}$
