Mass of a spherical cap with height-proportional density ($M=\frac{\pi k}{4}(R^2-c^2{)}^2$)

For a solid spherical cap $r^2+z^2\le R^2$, $z\ge c$, where $0\le c\le R$ and the mass density is $\rho =kz$ with $k\ge 0$, a volume integral in cylindrical coordinates givesHere the height is measured from the centre of the sphere, rather than from the bottom of the cap. Specifying that origin matters for a nonuniform mass density.