Question 30899
In order to answers this question, you need to know the formulae for the surface area (SA) and volume (V) of a sphere:

{{{SA = 4pi*r^2}}}
{{{V=(4/3)pi*r^3}}}
where r is the radius.

So given the surface area, we can calculate the radius, and given the radius, we can find the volume. We have:


{{{SA = 4pi*r^2=4536}}}
{{{r^2 = 4536/(4pi)}}}
{{{r = sqrt(4536/(4pi)) = 18.999}}}

So a sphere with an SA of 4536 cm^2 must have a radius of 18.999... cm. Now we just plug this value into the volume formula in order to find the volume:

{{{V=(4/3)pi*r^3=(4/3)pi*(18.999)^3= 28726.54}}}

So the volume of this shpere is 28,726.54 cm^3


I hope this helps!

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