It seemsobviousthat the volumeof the cylinderis greaterthan the othertwo figures.That’s becausethe
pyramidand conetaperoff to a singlepoint,whilethe cylinder’s sidesstay the samewidth.
Determiningwhetherthe pyramidor the conehas a greatervolumeis not so obvious.If you look at the
basesof eachfigureyou see that the apothemof the hexagonis congruentto the radiusof the circle.You
can see the relativesize of the two basesby superimposingone onto the other.
Fromthe diagramyou can see that the hexagonis slightlylargerin area than the circle.So it followsthat
the volumeof the right hexagonalregularpyramidwouldbe greaterthan the volumeof a right circularcone.
And indeedit is, but only becausethe area of the baseof the hexagonis slightlygreaterthan the area of
the baseof the circularcone.
The formulafor findingthe volumeof eachfigureis virtuallyidentical.Bothformulasfollowthe samebasic
form:
Sincethe baseof a circularconeis, by definition,a circle,you can substitutethe area of a circle, for
the baseof the figure.This is expressedas a volumepostulatefor cones.
Volumeof a RightCircularConeGivena right circularconewith height and a base
that has radius :Example 6
Find the volumeof a right conewith a radiusofcm and a heightof