Question 726739: A right rectangular prism with dimensions 2/3in. by 4/3in. by 8/3in. is enlarged by a scale factor of 1 1/2.
Q: The surface area of the original prism is ___ times as much as the surface area of the larger right rectangular prism.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Such an evil problem! It's trying to trick us two ways.
The shoebox-like prism has a length, L, a width, W, and a height, H, that are all fractional quantities of inches.
However, those numbers do not matter, given the question at the end.
When you enlarge dimensions by a factor of  ,
the surface area of a solid changes by a factor of  and the volume by a factor of  .
That happens because you have to multiply pairs of dimensions to get surface area, so when you multiply each pair, you get an as a factor.
A face that had an area of  gets it changed to  .
A face that had an area of  gets it changed to  .
A face that had an area of  gets it changed to  .
The scale factor was 
The dimensions of the large prism are  of the dimensions of the small one.
The dimensions of the small prism are  = of the dimensions of the large one.
The surface area of the original (smaller) prism is  times as much as the surface area of the larger right rectangular prism.
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