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# Diameter of a circle made up of multiple various sized circles

First I will give you the practical application.
I am trying to figure out the formula for finding the diameter of a cable that is made up of various size wires.
In math terms:
I have 8 circles that have a diameter of .04", I have 4 circles that have a diameter of .10" and I have 1 circle that has a diameter of .13".
I am trying to find the formula for figuring out what the diameter is of the smallest circle that all of the above circles could fit in.
I know how to figure it out if all the circles where the same size:
D=SQRRT((4xNxA)/3.1415)
N=NUMBER OF CIRCLES
A= AREA OF ONE CIRCLE

This works if all circles are the same, but I am not sure how to handle it if there are different size circles.
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CJSilver
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Author Commented:
Never mind, I answered my own question. I don't know why it took me so long to see it.

Formula D=SQRRT((4((NxA)+(N1xA1)+(N2+A2)))/p)

where N1, A1 is just the next group of circles
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Commented:
Assuming you mean (N2xA2), that's a lower bound,
but if the circles remain circles, there will be additional gaps between them,
If all the circles are the same size, the maximum, packing density is pi/6*sqrt(3) but how close you can get to that depends on the number of circles in a complicated way that no one understands completely.
With different sized circles, they can fill in each others gaps to get closet to a packing density of 1, but again, the exact umber is not known for other than a few special cases.
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Author Commented:
I am just trying to get an approximation. I have different size wires (i.e the circles) that I need to make up into a cable. I need to find out in advance approximately what the diameter of the cable will be.

I did mean N2xA2. From practical experience, the formula I listed above seems to come pretty close to approximating the correct diameter. Depending on how the wires lay in the cable will change the diameter. If my approximation is within 10% of the actual diameter then that is an acceptable deviation.
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