An Example of "Graphical Exaggeration"

Three-dimensional images may seem to be in proper proportion when they actually are not.

First, consider a (1-dimensional) line segment.

If we double the scale, then the resulting
line segment will truely be twice as long.

 
Next, consider a (2-dimensional) square.
If we double the scale, then the resulting square is
twice as long in both dimensions.  So the area will
more than double. In fact it's 2x2=4 times as much
i.e. "2-squared."                                               .



Finally, consider a (3-dimensional) cube.

If we double the scale, then the resulting cube is
twice as long in all 3 dimensions.  So its volume
is 2x2x2=8 times as much as the original cube is
i.e. "2-cubed."                                              .



Suppose a company decides to illustrate that its profits have doubled by showing a small money bag (representing their previous profit) next to a double scaled money bag (representing their recent profit).  While it may seem okay because the bigger bag is twice as tall, we must keep in mind that it is also twice as wide and twice as deep.

The depth is only a perception, because the images would be printed on a paper surface.  Note that even though the images are shown on a 2-dimensional paper surface, as with a photograph, the objects pictured are of course 3-dimensional.
           
Problem:  If the smaller bag contains $3,000 (and both bags have the same proportions of bill and coin denominations), then what would be the dollar value contained in the double scaled bag?