The volumesof two objectsare equalif the areasof theircorrespondingcross-sectionsare in all cases
equal.Two cross-sectionscorrespondif they are intersectionsof the figurewith planesequidistantfrom a
chosenbaseplane.
Example 1
Prove(informally)that the two circularconeswith the sameradiusand heightare equalin volume.As before,we can breakdownthe right circularconeinto disks.Now shift the disksover.You can see that the shifted-overfigure,sinceit usesthe very samedisksas the straightfigure,musthave
the samevolume.In fact, you can shift the disksany way you like. Sinceyou are alwaysusingthe same
set of disks,the volumeis the same.
Keepin mindthat Cavalieri’s Principlewill workfor any two solidsas long as their basesare equalin area
(not necessarilycongruent)and their crosssectionschangein the sameway.
Example 2