Volume shared by two perpendicular unit cylinders

Two infinite circular cylinders, each of radius $1$, have axes that meet at a right angle. What is the volume of the region lying inside both?

$16/3$. Put the axes along the $x$- and $y$-directions, so the solids are $y^2+z^2\le1$ and $x^2+z^2\le1$. At height $z$ the cross-section is a square of side $2\sqrt{1-z^2}$, area $4(1-z^2)$, and $\int_{-1}^{1}4(1-z^2)\,dz=\tfrac{16}{3}$.