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Broken Geometry (Cylindar) Fit Inside a Box 
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#1
Dec2012, 05:58 AM

P: 36

I have a pretty simple math problem that has been giving me the biggest headache. So what I need to do is optimize the space that I am using. Thus I have a piece that can be seen like a 20 inch in diameter cylinder that is 6 inches tall. I would like to be able to break it into as few pieces as possible but it is not the end of the world, nothing superglue or epoxy can not fix. So I have this cylinder that needs to fit entirely into a box. The box is 16 inches tall by 14 inches wide by 12 inches deep (16x14x12). I can easily fit the one cylinder into 2 boxes but the goal is one box.
I have not found a way to do it yet. I am also not sure if there is a nice formulaic way to solve this kind of problem but I am suspecting there is. Finally, there are 2 different adaptations that can be made to the cylinder if it would make it substantially easier to fix into the one box. The first which is an easier change is making the cylinder only 5.5 inches tall. This is preferred due to ease. The only other thing that could be do is to make the cylinder 17 inches in diameter. If possible I don't want to make these changes but if making them is the only way to make it fit then I might have to do that. Please help me. With your answer the orientation and sizes are important. Thanks in advance. Additionally if there is a cool math formula that will allow me to do some analytic like this that would be awesome. I can foresee needing to devise creative ways to make things fit into this same box in the near future. 


#2
Dec2012, 08:19 AM

Mentor
P: 11,928

I don't think there is a general formula/method.
In your specific example, it is easy: The height of the box is twice the height of the cylinder, this allows to stack parts in two layers in the box and the problem gets twodimensional. I attached a solution with three parts (the third piece gets the second layer in the box). It cannot work with two parts. 


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