The prismmay appearto be greaterin volume.But how can youprovethat the volumeof the prismis greater
than the volumeof the pyramid?Put one figureinsideof the other. The figurethat is smallerwill fit insideof
the otherfigure.
This is shownin the diagramon the above.Bothfigureshavecongruentbasesand the sameheight.The
pyramidclearlyfits insideof the prism.So the volumeof the pyramidmustbe smaller.
Example 4
Showthat the volumeof a squareprismis greaterthan the volumeof a squarepyramid.Drawor makea squareprismand a squarepyramidthat havecongruentbasesand the sameheight.Now placethe one figureinsideof the other. The pyramidfits insideof the prism.So whentwo figureshave
the sameheightand the samebase,the prism’s volumeis greater.
In general,whenyou comparetwo figuresthat havecongruentbasesand are equalin height,the prismwill
havea greatervolumethan the pyramid.