A spherical ring$\_$is a sphere with a cylindrical hole cut so that the centers of the cylinder and sphere coincide, also called a napkin ring.

Suppose the sphere has radius $R$ and the cylinder radius $r,$ and let $S=$ total surface area of the ring $($inside and outside combined$).$

Choose All the Correct Answers Below

$S=4R^2\sqrt[\phantom{2}]{(R^2-r^2)}$

$S=4(Rr)\sqrt[\phantom{2}]{(R^2-r^2)}$

If $R=5$ and $r=4$ then $S=108$

If $R=5$ and $r=4$ then $S=300$

If $R=5$ and $r=4$ then $S=192$

If $R=5$ and $r=4$ then $S=80$

$S=4r^2\sqrt[\phantom{2}]{(R^2-r^2)}$

$($H$)$ If $r0,$ then $S4R^2$

$(1)$ If $rR,$ then $S0,$ and the ring vanishes!