SOLUTION: A metal sphere of radius 9 is melted and transformed into three identical spheres. What are the radii of these spheres? What is the ratio of the area of one of these spheres to th

Algebra ->  Volume -> SOLUTION: A metal sphere of radius 9 is melted and transformed into three identical spheres. What are the radii of these spheres? What is the ratio of the area of one of these spheres to th      Log On


   

Question 1106588: A metal sphere of radius 9 is melted and transformed into three identical spheres.
What are the radii of these spheres? What is the ratio of the area of one of these spheres to the area of the original sphere?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A metal sphere of radius 9 is melted and transformed into three identical spheres.
Find the volume of the original sphere
V = 4%2F3pi%2A9%5E3
V = 3053.628 cu/cm
then
3053.628%2F3 = 1017.876 cu/cm is the volume of the smaller spheres
:
What are the radii of these spheres?
4%2F3pi%2Ar%5E3 = 1017.876
4%2Api%2Ar%5E3 = 3(1017.876)
r%5E3 = 3053.628%2F%284%2Api%29
r%5E3 = 243
r = 243%5E%281%2F3%29
r = 6.24 cm
:
What is the ratio of the area of one of these spheres to the area of the original sphere?
%284%2Api%2A6.24%5E2%29%2F%284%2Api%2A9%5E2%29
cancel 4pi
%286.24%5E2%29%2F%289%5E2%29 = 38.94%2F81 ~ 39%2F81
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