Among them: the side length of large square paper is 20cm；; X is the side length (cm) of the cut small square, 0.

(3) Maximum volume calculation. If the side length of the cut small square changes in turn according to the integer value, that is, 1 cm, 2 cm, 3 cm, 4 cm, 5 cm, 6 cm, 7 cm, 8 cm, 9 cm, 10 cm, the volume application formula of the folded rectangular box without cover is obtained.

It can be seen from Table 1 and Figure 5 that when the side length of the small square is less than 3cm, the volume of the uncovered cuboid box calculated by method 1 increases gradually; The volume reaches the maximum between 3 and 4 cm, and then decreases with the increase of the side length of the small square. When the side length of a small square is 10cm, the volume is 0. In order to further calculate the maximum volume, when the side length of the small square is 3~4cm, the volume of the uncovered rectangular box is calculated in steps of 0. 1cm.

As can be seen from Table 2 and Figure 6, when the side length of the small square is less than 3.3cm, the volume of the rectangular box without cover increases gradually; The volume reaches the maximum between 3.3 and 3.4 cm, and then decreases with the increase of the side length of the small square. By analogy, when the uncovered cuboid box is calculated in steps of 0.0 1cm and 0.00 1cm, ... is between 3.3 and 3.4 cm, it can be obtained that when the side length of the small square is 3.33333333 ... (that is, 0 of 65438+3/3),

(2) Volume calculation formula Volume calculation formula Volume calculation formula The above (4) and (5) are the same as the volume calculation formula of the "nine-grid" cutting method, as shown in formula (2): V=X*(20-X)*( 10-X) (2) where: the side length of a large square paper. X is the width of the cut rectangle (cm), 0.

0.5cm180.5cm 31.0cm 324cm31.5cm 433.5cm 2.0cm 512cm3.5cm 562.5cm 3.0cm 588cm 5cm 591.5cm 4.0cm. .5cm 544.5cm 35.0cm 500cm 35.5cm 445.5cm 36.0cm 384cm3.

I found that the cuboid has the smallest volume when the side length of a small square is 0.5 cm, and the cuboid has the largest volume when the side length of a small square is 3.5 cm. Moreover, when the side length of the cut square is an integer, the volume of the cuboid is also an integer, and when the side length of the cut square is a decimal, the volume of the cuboid is also a decimal.

(3)

When the side length of the small square is 3.5 cm, the volume of the uncovered cuboid is the largest, and the volume of the uncovered cuboid is 59 1.5 cubic cm.