Answer
$\pi(R^2-\frac{h^2}{4})h.$
Work Step by Step
We know that the volume of the cylinder is $\pi r^2h$, where $h$ is the height, $r$ is the radius of the base.
Also, the Pythagorean Theorem says that for a right triangle (if $z$ is the hypotenuse and $x,y$ are the other sides): $x^2+y^2=z^2$.
Hence here: $r^2+(\frac{h}{2})^2=R^2\\r^2=R^2-\frac{h^2}{4}$
Therefore $V=\pi r^2h=\pi(R^2-\frac{h^2}{4})h.$
