SOLUTION: My problem has to do with changing a sphere, with a S.A of 4536cm^2, to a volume. I know how to find the the S.A., but I am a little confused on how to change this to a volume answ

Algebra ->  Volume -> SOLUTION: My problem has to do with changing a sphere, with a S.A of 4536cm^2, to a volume. I know how to find the the S.A., but I am a little confused on how to change this to a volume answ      Log On


   

Question 30899: My problem has to do with changing a sphere, with a S.A of 4536cm^2, to a volume. I know how to find the the S.A., but I am a little confused on how to change this to a volume answer. My assignment for this question is titled "Find the volume of each sphere. Round to the nearest tenth." I have a picture of a solid round shape with the indicated S.A. I mentioned above. I don't mean to rush, but I do need this asap.
Thanks for your help
Answer by mbarugel(146) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Ar%5E2
V=%284%2F3%29pi%2Ar%5E3
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%2Ar%5E2=4536
r%5E2+=+4536%2F%284pi%29
r+=+sqrt%284536%2F%284pi%29%29+=+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=%284%2F3%29pi%2Ar%5E3=%284%2F3%29pi%2A%2818.999%29%5E3=+28726.54
So the volume of this shpere is 28,726.54 cm^3

I hope this helps!
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