Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2010 / Paper 2 / 18 / c

In cylindrical coordinates, the two surfaces meet when $9-r^2=r^2$, giving $r=3/\sqrt{2}$ and $z=9/2$. The solid has $0\le r\le 3/\sqrt{2}$, $0\le \theta \le 2\pi$, and $r^2\le z\le 9-r^2$. With volume element $rdzdrd\theta$,The upper-minus-lower height is nonnegative throughout that radial interval.