The reasonshouldbe obvious.At the “bottom,”both figuresstart out the same—witha squarebase.But
the pyramidquicklyslantsinward,“cuttingaway”largeamountsof materialwhilethe prismdoesnot slant.
Findthe Volumeof a Pyramidand Prism
Giventhe figureabove,in whicha squarepyramidis placedinsideof a squareprism,we now ask: how
manyof thesepyramidswouldfit insideof the prism?
To find out, obtaina squareprismand squarepyramidthat are both hollow, both haveno bottom,and both
havethe sameheightand congruentbases.
Now turn the figuresupsidedown.Fill the pyramidwith liquid.How manyfull pyramidsof liquidwill fill the
prismup to the top?
In fact, it takesexactlythreefull pyramidsto fill the prism.Sincethe volumeof the prismis:
where standsfor the area of the baseand is the heightof the prism,we can write:
or: