Optimizing Surface Area for Cornflakes Box Design

[chemical]

I have been given a problem of taking an object (I used a Cornflakes Box) and finding the optimal surface area compared to its volume (volume and ratio between sides constant)

I got:

Cornflakes Box :
Length = 25cm
Height = 36 cm
Width = 9 cm

Optimal Surface area box:
Length = 17.3 cm
Height = 43.28 cm
Width = 10.82

Overall a 90cm^2 difference in surface area.

Now I have to explain why Cornflakes would make a box with a greater surface area, thus costing more. Please help


The teacher also said something about the Golden Ratio, but i can't see any relation to this in the dimensions

 

[robphy]

Some ideas. (I don't know the real answer.)

Is the Corn Flakes box

• just right for the average [child's] hand to hold?
• more stable against tipping over?
• better for packing/tiling?
  (Interesting: http://www.scamecanica.com/qpm/examples/ )
• better for occupying more advertising space on your grocer's shelf?

 

[Locrian]

I'm going to go with door #2 robphy.

 

[Nenad]

Ill give you the golden ratio: 1:1:1 (a CUbe)

what don't you get about which one would cost more. The box with the larger surface ares costs more. Its that simple.

 

[Tom McCurdy]

But who wants to pour cereal out of a cube-- plus its built into the mind of the consumer that that is the shape. It has all to deal with appeal to the consumer.

 

[HallsofIvy]

Ill give you the golden ratio: 1:1:1 (a CUbe)

what don't you get about which one would cost more. The box with the larger surface ares costs more. Its that simple.

No, that is not the golden ratio. And if you had read the original post, the question was WHY would the cereal makers use a box that cost more. You appear to be saying that cereal makers use a box with more area BECAUSE it costs more. Do you really think they enjoy paying more money?

 

[Nenad]

No, that is not the golden ratio. And if you had read the original post, the question was WHY would the cereal makers use a box that cost more. You appear to be saying that cereal makers use a box with more area BECAUSE it costs more. Do you really think they enjoy paying more money?

the golgen ratio IS 1:1:1. The only reason the companies don't make it this is because of appeal, advertisement and other factors.

 

[chemical]

the golgen ratio IS 1:1:1. The only reason the companies don't make it this is because of appeal, advertisement and other factors.

1:1:1 is the optimal ratio, not the golden ratio. Thanks for the comments guys :)

 

[HallsofIvy]

the golgen ratio IS 1:1:1. The only reason the companies don't make it this is because of appeal, advertisement and other factors.

It may be the "golgen" ratio but it certainly isn't the "golden ratio".