It shouldbe clearfrom the diagramthat the total volumeof the disksis equalto the volumeof the original
cylinder.
Now start with the sameset of disks.Shift eachdisk over to the right.The volumeof the shifteddisksmust
be exactlythe sameas the unshifteddisks,sinceboth figuresare madeout of the samedisks.
It followsthat the volumeof the obliquefigureis equalto the volumeof the originalright cylinder.
In otherwords,if the radiusand heightof eachfigureare congruent:
The principleshownabovewas developedin the seventeenthcenturyby ItalianmathematicianFrancisco
Cavalieri.It is knownasCavalieri’s Principle.(Liu Hui also discoveredthe sameprinciplein third-century
China,but was not givencreditfor it until recently.) The principleis valid for any solid studiedin this chapter.
Volumeof a SolidPostulate(Cavalieri’s Principle):