If we take a cylinder of height $2x$ and radius $x$, as well as a sphere of radius $x$, we notice that they have the same curved surface area.
Also, if we take the frustum of a cone such that it has base radii $R$ and $r$ ($R>r$) and slant height $l$, and we take a complete cone with base radius $R+r$ and slant height $l$, we notice that they have the same curved surface area.
Is there any simple logical reason why this happens?
Of course, one logical proof would be to simply derive the respective formulae and substitute the values. That would still imply that these are just coincidences. Is there any simpler method, preferably a somewhat visual one from which it becomes obvious why these instances occur?