what is the ratio of volumes of
cone : sphere : cylinder
in its simplest form?
establish that the volume of the sphere plus the cone make the volume of the cylinder
(image on Wikimedia)
this result was established by Archimedes using small slices, as explained in 'Cut the Knot' and illustrated here
there's an interesting illustration below (also the above diagram) and an explanation of Archimedes' method on a blog by Zachary Abel
cone + hemisphere = cylinder
which solid has the smallest volume?