SOLUTION: The ratio of the volume of two spheres is 8:27. What is the ratio of the lengths of the area of these two spheres?
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Question 1139791: The ratio of the volume of two spheres is 8:27. What is the ratio of the lengths of the area of these two spheres? Found 2 solutions by Alan3354, greenestamps:Answer by Alan3354(69443) (Show Source):
Your question doesn't make any sense; so I don't know what you were asking....
The ratio of volumes is 8:27 = (2^3):(3^3).
Since all spheres are similar, that means
(1) the ratio of any measurements of length on the two spheres is 2:3; and
(2) the ratio of area measurements on the two spheres is (2^2:(3^2).
This is an example of a very powerful general concept regarding similar figures.
In any two similar figures, if the ratio of linear measurements (scale factor) is a:b, then the ratio of area measurements is (a^2):(b^2), and the ratio of volume measurements is (a^3):(b^3).
