On a rectangular sheet of iron 20 decimeters in length and 12 decimeters in width, a cylindrical sheet of iron with a diameter of 2 decimeters should be cut out. At most, several circles can be cut out The sum of the edge lengths of a rectangle is 72. Given that the length is 1.5 times the width and the width is 2 times the height, the volume of a rectangle can be obtained

On a rectangular sheet of iron 20 decimeters in length and 12 decimeters in width, a cylindrical sheet of iron with a diameter of 2 decimeters should be cut out. At most, several circles can be cut out The sum of the edge lengths of a rectangle is 72. Given that the length is 1.5 times the width and the width is 2 times the height, the volume of a rectangle can be obtained

The length direction can intercept 20 △ 2 = 10;
The width direction can intercept 12 △ 2 = 6;
It can intercept 10 × 6 = 60 at most;
4 × (L + W + H) = 72
1.5 × width + 2 × height + height = 72 △ 4
1.5 × 2 × H + 2 × H + H = 18
6 × height = 18
Height = 18 △ 6 = 3;
Width = 2 × height = 6,
Length = 1.5 × width = 9;
Volume = length × width × height = 9 × 6 × 3 = 162;