Let the length, width and height of the box be x, y, z, y and z (unit: cm) respectively.
Then XYZ = 1000, ... (1)
Now we only need the minimum surface area of the box, which is the minimum value of xy+yz+xz.
Obviously, x, y, z, y and z are all positive integers,
We have1000 = 2 * 2 * 250 = 2 * 4 *125 = 2 * 5 *100 = 2 * 20 * 25 = 4 * 5 * 50 = 4 *10.
Because you want to design a rectangular box, it cannot be10x10x10.
Finally, after calculation, the box of 5* 10*20: 350cm? At the very least,
This calculation is really no trouble, 5 minutes is enough.
Therefore, the box is designed to be 5* 10*20, which is the most paper-saving and conforms to the meaning of the question.
In fact, there is no need to list them one by one, the product is certain, the smaller the difference, the smaller the sum,
Although it is not rigorous to use, it should be applicable. It just makes sense.
The above situation is covered. If the design is of course more paper-saving without a cover, it can only be listed.
I hope it inspires you.