Volume shared by two crossing unit cylinders

Two solid cylinders, each of radius $1$, have axes that meet at a right angle. Find the volume of the region lying inside both.

$16/3$. With axes along $x$ and $y$, the solid is $x^2+z^2\le1$, $y^2+z^2\le1$. A horizontal slice at height $z$ is a square of side $2\sqrt{1-z^2}$, so the volume is $\int_{-1}^{1}4(1-z^2)\,dz=\tfrac{16}{3}$.