Posted by John on .
Use this proportionality: A correlation V square 2/3
How much more material is needed to manufacture an industrial plastic container with twice the volume of a similar container?
A manufacturer of plastic containers prices its product by the amount of plastic used to make the container (surface area). A particular container costs $12. How much would you expect a container with eight times the volume to cost?
I needed to know the lay out. I also was wondering how to do a graph for this problem?

Algebra 
drwls,
You don't need a graph. For eight times the volume, the linear dimensions would be larger by a factor of cube root of 8 = 2. The areal dimensions would be higher by a factor of 2^2 = 4. Cost would increase by the same factor, assuming the thickness of the container wall material does not change.
The cost would be $48.
Another way of saying it is that area is proportional to the 2/3 power of volume. That may be what you were trying to say in the beginning.