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Make a rectangular box as big as possible without a lid.
How to make a rectangular box without a lid from a square piece of paper? How can I make a rectangular box without a cover as large as possible?

To make a rectangular box without a lid from a square piece of paper, first cut out a square with the same area at the four corners of the square paper, and then fold it. If the side length of this square paper is A and the side length of the cut small square is B, through repeated experiments and calculations, I find that when a:b=6: 1, the volume of the folded rectangular box is the largest. Now let's check:

① When a =30cm,

B (cm)

2

three

four

five

six

seven

eight

nine

roll

cubic centimeter

1352

1728

1936

2000

1944

1792

1568

1296

Therefore, when b=5cm, the uncovered rectangle has the largest volume, and b:a= 1:6.

② When a= 18cm,

B (cm)

1

2

three

four

five

six

seven

eight

roll

cubic centimeter

256

392

432

celebrity

320

2 16

1 12

32

As can be seen from the above table, when b=3cm, the uncovered rectangle has the largest volume, and b:a= 1:6.

In order to make the answer more accurate, we now round B to the tenth place.

b

(cm)

2.5

2.7

2.9

3. 1

3.3

3.5

roll

cubic centimeter

422.5

428.652

43 1.636

43 1.644

428.868

423.5

Interested parties can calculate percentiles and thousandths. In short, when a:b= 1:6, the volume of the folded rectangular box without cover is the largest.

Hope to adopt! ! ! -