Cones
LearningObjectives
- Find the surfacearea of a coneusinga net or a formula.
- Find the volumeof a cone.
Introduction
A coneis a three-dimensionalfigurewith a singlecurvedbasethat tapersto a singlepointcalledanapex.
The baseof a conecan be a circleor an oval of sometype.In this chapter, we will limit the discussionto
circularcones.The apexof a right conelies abovethe centerof the cone’s circle.In an obliquecone,the
apexis not in the center.
The heightof a cone, , is the perpendiculardistancefrom the centerof the cone’s baseto its apex.
SurfaceAreaof a ConeUsingNets
Mostthree-dimensionalfiguresare easyto deconstructinto a net. The coneis differentin this regard.Can
you predictwhatthe net for a conelookslike? In fact, the net for a conelookslike a smallcircleand a sector,
or part of a largercircle.
The diagramsbelowshowhow the half-circlesectorfoldsto becomea cone.
Notethat the circlethat the sectoris cut from is muchlargerthan the baseof the cone.
Example 1