Dimensions of box that minimize the material used

In summary, when minimizing material usage for a box, using equal dimensions for length, width, and height is generally the most efficient. The shape of the box can also greatly impact material usage, with irregular or complex shapes typically requiring more material. There are formulas available to calculate the optimal dimensions for a specific material, taking into account factors such as volume, surface area, and material thickness. Additionally, other factors such as purpose, contents, and practicality should be considered when determining box dimensions.
  • #1
Winzer
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Homework Statement


A box with a square base and open top must have a volume of 32,000cm^3. Find the dimensions of the box that minimize the amont of material used.

Homework Equations


[tex]Sa(surface area)=4xy+x^2[/tex]
[tex]Volume=x^2y[/tex]

The Attempt at a Solution


I want to minimize Sa I am pretty sure so how do i begin?
 
Last edited:
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  • #2
Never mind I figured it out.
 

1. What are the dimensions of a box that minimize the material used?

The dimensions of a box that minimize the material used can vary depending on the specific material and design of the box. However, in general, a box with equal length, width, and height will use the least amount of material.

2. How does the shape of a box affect the amount of material used?

The shape of a box can greatly impact the amount of material used. Boxes with irregular shapes or multiple compartments may require more material to be sturdy and functional compared to a simple rectangular box.

3. Is there a formula for calculating the dimensions of a box that minimizes material used?

Yes, there are formulas that can be used to calculate the dimensions of a box that minimize material used. These formulas take into account the volume of the box, the surface area, and the thickness of the material being used.

4. How can I determine the optimal dimensions for a specific material?

The optimal dimensions for a specific material can be determined by using the appropriate formulas and considering factors such as the strength and durability of the material, as well as the desired size and shape of the box.

5. Are there any other factors to consider besides material usage when determining box dimensions?

Yes, besides material usage, there are other factors to consider when determining box dimensions. These include the purpose of the box, the weight and fragility of the contents, and any additional features such as handles or closures. The dimensions should also be practical and suitable for storage and transportation.

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