SOLUTION: Tow objects with volumes of 54cm3 and 108cm3. Find the ratio of the surface areas. All of the problems that we have had in the past have a whole number as an answer. When I tried

Algebra ->  Surface-area -> SOLUTION: Tow objects with volumes of 54cm3 and 108cm3. Find the ratio of the surface areas. All of the problems that we have had in the past have a whole number as an answer. When I tried      Log On


   

Question 194000: Tow objects with volumes of 54cm3 and 108cm3. Find the ratio of the surface areas.
All of the problems that we have had in the past have a whole number as an answer. When I tried to solve this one I get 3.77976 for 54cm3 and 4.76220 for 108cm3. How do I convert it to a fraction or is there a step that I am missing?
Answer by Alan3354(69443) About Me  (Show Source):
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Tow objects with volumes of 54cm3 and 108cm3. Find the ratio of the surface areas.
All of the problems that we have had in the past have a whole number as an answer. When I tried to solve this one I get 3.77976 for 54cm3 and 4.76220 for 108cm3. How do I convert it to a fraction or is there a step that I am missing?
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Assuming the objects are similar (if not, there's no answer):
Volume is a function of the 3rd power.
Area is a function of the 2nd power.
2x the volume --> 2^(2/3) x the area.
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Take it as 2 spheres:
V+=+4%2Api%2Ar%5E3%2F3
r1+=+%283V%2F%284%2Api%29%29%5E%281%2F3%29%29
r1+=+%283%2A108%2F4pi%29%5E%281%2F3%29
r1 = ~ 1.861051473
r2 = ~ 1.477117533
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Area+=+4%2Api%2Ar%5E2
A1 = ~ 43.52378277 sq cm
A2 = ~ 27.418265 sq cm
A1/A2 = 2^(2/3) = cube root of 4