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? Express answer as

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Question 257144: 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? Express answer as 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 1:64, respectively.
What is the ratio of the surface area of solid A to the surface area of solid B? Express answer as a common fraction.
:
Use cubes for simplicity, with sides, x & y
x%5E3%2Fy%5E3 = 1%2F64
y^3 = 64x^3
Cube root of both sides
y = 4x
:
Surface area
%286x%5E2%29%2F%286y%5E2%29
Cancel 6
x%5E2%2Fy%5E2
Replace y with 4x
x%5E2%2F%28%284x%29%5E2%29 = x%5E2%2F%2816x%5E2%29 = 1%2F16