CK12 - Geometry

Whichsectorwill give you a tallercone—ahalf circleor a sectorthat coversthree-quartersof a circle?As-
sumethat both sectorsare cut from congruentcircles.

Makea modelof eachsector.

The half circlemakesa conethat has a heightthat is aboutequalto the radiusof the semi-circle.

The three-quarterssectorgivesa conethat has a widerbase(greaterdiameter)but its heightas not as
greatas the half-circlecone.

Example 2

Predictwhichwill be greaterin height—aconemadefrom a half-circlesectoror a conemadefrom a one-
third-circlesector. Assumethat both sectorsare cut from congruentcircles.

The relationshipin the exampleaboveholdstrue—thegreater(in degrees)the sector, the smallerin height

of the cone.In otherwords,the fraction is less than , so a one-thirdsectorwill createa conewith
greaterheightthan a half sector.

Example 3

Predictwhichwill be greaterin diameter—aconemadefrom a half-circlesectoror a conemadefrom a
one-third-circlesector. Assumethat the sectorsare cut from congruentcircles

Hereyou havethe oppositerelationship—thelarger(in degrees)the sector, thegreaterthe diameterof the

cone.In otherwords, is greaterthan , so a one-halfsectorwill createa conewith greaterdiameter
than a one-thirdsector.

SurfaceAreaof a RegularCone

The surfacearea of a regularpyramidis givenby: