SOLUTION: Hi, everyone. Can anyone help me with this question, please? The volumes of two similar solids are {{{ 1331 m^3 }}} and {{{ 343 m^3 }}}. The surface area of the larger one is {{

Algebra ->  Volume -> SOLUTION: Hi, everyone. Can anyone help me with this question, please? The volumes of two similar solids are {{{ 1331 m^3 }}} and {{{ 343 m^3 }}}. The surface area of the larger one is {{      Log On


   

Question 1115783: Hi, everyone. Can anyone help me with this question, please?
The volumes of two similar solids are +1331+m%5E3+ and +343+m%5E3+. The surface area of the larger one is +484+m%5E2+. What is the surface area of the smaller solid?
The answer choices are: (A) 1372, (B) 196, (C) 343, and (D) None of the above.
Thus far, I have gotten multiple different answers, but my best guess is in answer D.
Your help would be greatly appreciated!! Thanks so much! :)

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


In any similar figures, if the scale factor (ratio of linear measurements) 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.

In your problem, you are given
a%5E3%3Ab%5E2+=+1331%3A343+=+11%5E3%3A7%5E3

So the ratio of area measurements is
11%5E2%3A7%5E2+=+121%3A49

Then
484%3A121+=+x%3A49
or
484%2F121+=+x%2F49
4+=+x%2F49
x+=+196

Answer choice B.