Question about the minimum area

In summary, the conversation is about finding the minimum surface area of a container with a square base and a volume of 1000. The attempt at a solution involved using the equations A=x^2 and V=x^2*h, and differentiating to find the minimum area. It was eventually determined that the container should be a cube with dimensions of 10x10x10 to minimize the surface area.
  • #1
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Homework Statement


hi guys, how are you all,,
my friend had a quiz and he told me about this question :
container has a square base and the volume of it V= 1000 , find the minimum area of the surface that the container can have ...


Homework Equations


A=x^2 , V=x^2 * h


The Attempt at a Solution


i started by saying: 1000=x^2 * h then i can get h =1000/x^2 and A=x^2 then i differentiate 0=2x*h+x^2*h` ... i get at the end (2000/x)-(2000/x)=0 and this doesn't make any sense ,,i tried another way ,, i assumed it should be a cube for the minimum area so i get 6x^2=1000 then i get (x=13) is the answer right?? ,, is the question even right ?? anyone knows how it should be at least ??
 
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  • #2
By minimum area, do you mean the sum of the area of the six surfaces? Are there six, is the top included?
Often these questions are asked to minimise material for packaging to hold a certain volume which I'd say this question is about. Not sure though...
 
  • #3
i really don't know ,, he didn't remember ,, although, if it was the minimum area of the surface of the container ,, it should be cube right ?? so can i apply this equation ?
(6x^2=1000) ??
 
  • #4
i think i got it ,, can anyone check my answer now ,,

1000=x^2*y , y=1000/x^2 , surface area = 2x^2+4x*(1000/x^2) then differentiate i get 4x-(4000/x^2)=0 then i get x=10 and y=10 so it's cube alright :D
 

1. What is the concept of minimum area?

The concept of minimum area refers to the smallest possible surface or space that an object or material can occupy. It is often used in mathematical and scientific contexts to determine the most efficient use of resources.

2. How is minimum area calculated?

The calculation of minimum area depends on the specific context and variables involved. In general, it involves finding the smallest possible shape or arrangement that can contain or represent a given set of data or objects.

3. What is the significance of minimum area in science?

Minimum area is important in science because it allows for the optimization of resources and the understanding of efficiency in natural phenomena. It can also help in the design and development of new technologies and processes.

4. Can minimum area change over time?

Yes, minimum area can change over time as it is affected by various factors such as external conditions, technological advancements, and changes in data or variables. It is important to regularly reassess and update calculations of minimum area in order to maintain accuracy.

5. How does minimum area relate to sustainability?

Minimum area is closely related to sustainability as it involves minimizing the use of resources and maximizing efficiency. By understanding and implementing minimum area principles, we can reduce waste and environmental impact in various industries and processes.

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