Consider a solid ball of radius $R$. Cut a cylindrical hole, through the center of the ball, such that the remaining body has height $h$. Call this the donut $D(R,h)$. Use Cavalieri’s principle to calculate the volume of $D(R,h)$. Calculate the volumes of $D(25,6)$ and $D(50,6)$.
Several students have asked what $D(R,h)$ looks like. Here are some pictures that I found to illustrate the concept. The donut $D(R,h)$ is the region between the red sphere and blue cylinder. The golden balls below show various views of the donut. The donut should fit between the two planes $z=h/2$ and $z=-h/2$, so that it has total height $h$.