- A sphereresultswhenyou constructa polyhedronwith an infinitenumberof facesthat are infinitely
small.To see why this is true, recallregularpolyhedra.
As the numberof faceson the figureincreases,eachface gets smallerin area and the figurecomesmore
to resemblea sphere.Whenyou imaginefigurewith aninfinitenumberof faces,it wouldlook like (and be!)
a sphere.
Partsof a Sphere
As describedabove,a sphereis the surfacethat is the set of all pointsa fixeddistancefrom a centerpoint
. Terminologyfor spheresis similarfor that of circles.
The distancefrom to the surfaceof the sphereis , the radius.
Thediameter, , of a sphereis the lengthof the segmentconnectingany two pointson the sphere’s surface
and passingthrough. Notethat you can find a diameter(actuallyan infinitenumberof diameters)on
any planewithinthe sphere.Two diametersare shownin eachspherebelow.
Achordfor a sphereis similarto the chordof a circleexceptthat it existsin threedimensions.Keepin mind
that a diameteris a kind of chord—aspecialchordthat intersectsthe centerof the circleor sphere.