CK12 - Geometry

Now, it shouldbe obviousthat the sum of all of the basesof the pyramidsis simplythe surfacearea of the

sphere.Sinceyou knowthat the surfacearea of the sphereis , you can substitutethis quantityinto
the equationabove.

Finally, as increasesand the surfaceof the figurebecomesmore“rounded,” , the heightof each

pyramidbecomesequalto , the radiusof the sphere.So we can substitute for. This gives:

We can writethis as a formula.

Volumeof a SphereGivena spherethat has radius

Example 3

Find the volumeof a spherewith radius

m.

Use the postulateabove.

Example 4

A spherehas a volumeof

. Find its diameter.

Use the postulateabove.Convert to an improperfraction,