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?

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.

To determine how much more material is needed to manufacture an industrial plastic container with twice the volume of a similar container, we can use the concept of proportionality and the given correlation: A correlation V square 2/3.

Let's say the original container has a volume of V1. The container with twice the volume would have a volume of 2V1.

Using the given correlation, we have:

(2V1)^(2/3) = k * V1^(2/3)

Where k is a constant of proportionality.

To find k, we can use the fact that a particular container costs $12. If we substitute V1 = 1 into the equation:

(2)^(2/3) = k * 1^(2/3)

Simplifying the equation:

k = (2)^(2/3)

Now, let's apply this correlation to the second part of the question. We are given that a container with eight times the volume costs $12. This means we need to find the volume, V2, such that:

V2^(2/3) = k * (8V1)^(2/3)

Substituting the value of k we obtained earlier:

V2^(2/3) = (2)^(2/3) * (8V1)^(2/3)

Simplifying the equation:

V2 = 2 * 8V1

V2 = 16V1

Therefore, a container with eight times the volume (V2) would cost 16 times more than the original container. Since the original container costs $12, the container with eight times the volume would cost:

16 * 12 = $192.

To graph this problem, you can set up a graph with the volume (V) on the x-axis and the cost on the y-axis. Plot the data points for different volumes and their corresponding costs, and then draw a line or curve that best fits the data points. This will help visualize the relationship between volume and cost.