Broken Geometry (Cylindar) Fit Inside a Box

In summary, the problem is to fit a 20-inch diameter cylinder that is 6 inches tall into a box with dimensions 16x14x12 inches. The goal is to fit the cylinder into one box, although two boxes can be used if necessary. There are two possible adaptations to the cylinder, making it either 5.5 inches tall or 17 inches in diameter. However, there is no general formula or method for solving this type of problem. In this specific example, the height of the box is twice the height of the cylinder, allowing for two layers in the box. A solution with three parts is possible, but not with two parts.
  • #1
Badger33
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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.
 
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  • #2
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 two-dimensional.

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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What is "Broken Geometry (Cylindar) Fit Inside a Box"?

"Broken Geometry (Cylindar) Fit Inside a Box" is a scientific concept that refers to the ability of a cylindrical object to fit into a box with a different shape, such as a square or rectangle. This concept is often studied in geometry and physics.

What is the significance of studying "Broken Geometry (Cylindar) Fit Inside a Box"?

Studying "Broken Geometry (Cylindar) Fit Inside a Box" can provide insight into the relationship between the size and shape of objects and how they can fit together. This concept has practical applications in fields such as packaging and engineering.

What factors affect the ability of a cylindrical object to fit into a box?

The main factors that affect the ability of a cylindrical object to fit into a box include the diameter and length of the cylinder, as well as the dimensions and shape of the box. Additionally, the orientation of the cylinder and the presence of any obstructions inside the box can also impact the fit.

How is the fit of a cylindrical object into a box calculated?

The fit of a cylindrical object into a box can be calculated using mathematical formulas that take into account the dimensions and shape of both the cylinder and the box. These formulas typically involve calculating the volume of the cylinder and the volume of the space within the box, and then comparing the two values.

What are some real-world examples of "Broken Geometry (Cylindar) Fit Inside a Box"?

Examples of "Broken Geometry (Cylindar) Fit Inside a Box" can be found in various industries, such as shipping and storage. For instance, cylindrical objects like bottles and cans can be packed into rectangular boxes to save space and reduce shipping costs. This concept is also relevant in architecture, where cylindrical pipes and ducts must fit into square or rectangular spaces within buildings.

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