After four cubes of the same size are glued into a cuboid (as shown in the figure), the surface area is reduced by 54 square centimeters, and the surface area and volume of the cuboid are calculated

After four cubes of the same size are glued into a cuboid (as shown in the figure), the surface area is reduced by 54 square centimeters, and the surface area and volume of the cuboid are calculated

After four equal cubes are glued into a cuboid, the surface area is reduced by 54 square centimeters. Calculate the surface area and volume of the cuboid
P85-8 in the revised edition of daquanli in Beijing

There are two situations in this question
1) Four cubes are arranged in a row or a column. If the side length of the cube is a centimeter, the length, width and height of the cuboid are a, a and 6A respectively
At this time, six sides disappear because of overlapping, that is, the surface area is reduced by six cube side areas: 6xa square = 54
A = 3
So the surface area of the cuboid is a square x2 + ax6ax2 + ax6ax2 = 26xa square = 234 square centimeter
Cuboid volume = ax6a = 6x27 = 162 cubic centimeter
2) Four cubes are arranged in the form of 2x2. Let the side length of the cube be a centimeter, then the length, width and height of the cuboid are 2a, 2a and a respectively
There are 8 sides disappeared because of overlap, that is, the surface area is reduced by 8 cube side areas: 8xa square = 54
The solution is: a = 3x radical 3 / 2
So the surface area of the cuboid is = 2ax2ax2 + 2axax2 + 2axax2 = 16xa square = 108 square centimeter
Cuboid volume = 2axax2a = 8 = 81x root 3 / 2 cubic centimeter
I hope my answer will help you

After four cubes of the same size are glued into a cuboid, the surface area is reduced by 54 square decimeters, and the surface area and volume of the cuboid are calculated

After four cubes of the same size are glued into a cuboid, six faces are missing, and the surface area is reduced by 54 square decimeters. The area of one face is 54 / 6 = 9 square decimeters, and the side length is 3 decimeters. The surface area of the large cuboid is 4 * 6-6 = 18 faces, and 9 * 18 = 162 square decimeters
The volume of a small cube is 9 * 3 = 27 cubic decimeters, and that of a large cube is 9 * 3 * 4 = 108 cubic decimeters