Question 598762: 5. If the surface area of a cube is decreased by 19%, the volume of the cube decreases by
(A) 9%(B) 19%(C) 27.1%(D) 37.1%(E) 85.2%
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! If the side of a square is changed by a factor  }, the area will change by a factor  .
Since the surface of a cube is the surface of its 6 square sides, if the length of an edge of the cube is changed by a factor , the surface area of each side and the surface area the cube will change by a factor .
At the same time, if the length of an edge of the cube is changed by a factor }, the volume will change by a factor  .
A decrease of 19%, results in 81% (100%-19%) of the original amount.
If the surface area of a cube decreases by 19%, that area becomes 0.81 times what it originally was (81% of what it originally was).
The factor, k, for the change in the length of an edge of that cube is related to the factor (0.81) for the change in the surface area by the relation
 -->  -->  .
If the length of an edge of a cube changes by a factor , then the volume changes by a factor
 .
The volume would be 0.729 times the volume before the change, meaning 72.9% of the volume before the change, for a decrease of 100.0%-72.9%= %
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