SOLUTION: the volumes of two similar solids, A and B, are in the ratio 1:64,respectively.What is the ratio of the surface area of solid A to the surface area of solid B? Can you please expre

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Question 276252: the volumes of two similar solids, A and B, are in the ratio 1:64,respectively.What is the ratio of the surface area of solid A to the surface area of solid B? Can you please express it in a common fraction?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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the volumes of two similar solids, A and B, are in the ratio 64,respectively.
What is the ratio of the surface area of solid A to the surface area of solid B?
Can you please express it in a common fraction?
:
Assume they are cubes
Let x = side of the smaller
Let y = side of the larger
:
x%5E3%2Fy%5E3 = 1%2F64
cross multipl
y%5E3+=+64x%5E3
Find the cube root of both sides
y = 4x
:
Surface area ratio
6x%5E2%2F%286y%5E2%29
Replace y with 4x
6x%5E2%2F6%284x%29%5E2
Cancel the 6
x%5E2%2F%284x%29%5E2 = x%5E2%2F%2816x%5E2%29
cancel x^2
1%2F16 is the surface area fraction