1. Do this.

( 1)

Cut off the volume of a cuboid with square sides.

1cm 324cm3

2cm 512cm3

3 cm 588 cubic cm

4 cm 576 cubic cm

5 cm 500 cubic cm

6 cm 384 cubic cm

7 cm 252 cubic cm

8 cm 128 cubic cm

9 cm 36 cubic cm

10cm 0 cm3

(2)

I found that the cuboid has the smallest volume when the side length of the small square is 10 cm, and the cuboid has the largest volume when the side length of the small square is 3 cm.

(3)

When the side length of the small square is 3 cm, the volume of the uncovered cuboid is the largest, and the volume of the uncovered cuboid is 588 cubic centimeters.

Do it

( 1)

Cut off the volume of a cuboid with square sides.

0.5cm 180.5cm

1.0 cm 324 cm 3

1.5cm 433.5cm。

2.0cm 512cm3

2.5 cm 562.5 cubic cm

3.0 cm 588 cubic cm

3.5 cm 59 1.5 cm.

4.0 cm 576 cubic cm

4.5 cm 544.5 cubic cm

5.0 cm 500 cubic cm

5.5 cm 445.5 cubic cm

6.0 cm 384 cubic cm

…… ……

(2)

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.