Question 835815: how many spheres of diameter 1 cm can be made out of a sphere of area 324π.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if you are talking about volume, you will get one answer.
if you are talking about surface area you will get another answer.
here are the formulas for surface area and volume of a sphere.
http://math.about.com/od/formulas/ss/surfaceareavol.htm
i'll do volume first.
under the assumption that the total volume of the larger sphere is 324 * pi, you would probably calculate as follows:
the volume of the smaller sphere is equal to 4/3 * pi * r^3
the radius of the smaller sphere is equal to 1/2.
the volume of the smaller sphere is therefore equal to 4/3 * pi * (1/2)^3.
this would be equal to 1/6 * pi.
if you take 324 * pi and divide it by 1/6 * pi, you will get 1944 small spheres that have a total volume equal to 324 * pi cubic centimeters.
i'll do surface area next.
under the assumption that the total surface area of the larger sphere is 324 * pi, you would probably calculate as follows:
the surface area of the smaller sphere is equal to 4 * pi * r^2.
the radius of the smaller sphere is equal to 1/2.
the surface area of the smaller sphere is equal to 4 * pi * (1/2)^2.
this would be equal to pi.
if you take 324 * pi and divide it by pi, you will get 324 small spheres that have a total surface area equal to 324 * pi square centimeters.
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