How do you cut a cube into 20 small cubes and 53 cubes?

The number of small cubes in a large cube is determined by the fractions of the sides of the large cube for example, if it is divided into 2, there will be 8 small cubes, and if it is divided into 3, there will be 27 small cubes. The general formula divides the sides into n parts, and you get n times n and then n small cubes. i.e. n at the same time, the total number of points is subtracted by 1

Getting through Formula n -1

Divided into 20 Obviously 3 = 27, the total is 1 + 27 - 1 = 27 will not work.

It is divided into the smallest 2 equal parts, 2 = 8, 8 + 8-1 = 15 in two parts, and 15 + 8-1 = 22 in three parts. So you can't get 20.

Divided into 53 3 = 27 points, the first time 1 + 27 - 1 = 27 points, the second time 27 + 27 - 1 = 53 points.

Cut into 20 pieces

1.Cut 4 knives horizontally and divide into 5 layers.

2.Cut 3 more knives from top to bottom and divide into 4 columns, (i.e. now there are 4 columns and 5 layers), and now there are 20 pieces.

Cut into 53 pieces

1.Cut 3 knives horizontally and divide into 4 layers.

2.Then cut 12 knives from top to bottom and divide into 13 columns. (i.e. now there are 13 columns with 4 layers) 4Small cubes do not have to be the same size.

Take one of these 52 cubes and cut it once, it becomes 2 cubes, and now there are 53 small cubes.

6 knives. Think backwards and think about how 27 small cubes can form one big cube.

The way of 27 small cubes to form a large cube can only be the arrangement of 3 3 3, so the result is that the common edge of the composition of each face small cube is four, and the six sides have a total of 24 common edges, from the figure point of view, every four common edges form a closed line, so it is necessary to cut 24 4 = 6 knives.

Question: How do you cut a square into 9 small cubes?

It can be cut into 2*2*2=8 cubes, 3*3*3=81 small squares......How do you cut it into 9 pieces?

Let's say you cut it into 9 with one method.

It can be calculated in this way, there were originally 6 faces, and 9 small orange waiters had 9*6=54 faces, and 54-6=48 faces.

6. Cut two knives on the front and upper sides.

Select and cut 3 knives can be cut into 8 small squares, analysis: there are 8 small pieces before cutting the fourth knife, if the fourth knife can cut the eight small pieces can be cut to get 16 pieces, but a knife can not cut to 8 small pieces at the same time, only the cutting method as shown in the figure can be cut to 7 small pieces at the same time, that is, 8 + 7 = 15 pieces can be obtained after cutting).

The landlord will understand if you think about it more!

Cut 4 knives into 16 pieces, rows, 1 knife horizontally and vertically, into 4 pieces and then 1 knife longitudinally, into 8 pieces, the second knife longitudinally, into 16 pieces, 4 knives down can only 15 pieces, impossible.

Solution: Because, 8>4>3, take the smallest number of the length and width of the cuboid as the side length of the cube, then there is, the side length of the cube is 3cm

So the volume of the cube is: 3x3x3=27cm

Surface area: 3x3x6=54c

Sum of all side lengths: 3x12 = 36cm

solution, the base area of the cuboid.

25 (square centimeters) on the bottom side.

5 (cm) the length of a large cuboid.

5+=cm).

The surface area of a large box.

202 (square centimeters).

Assuming that the side length of the cube is 3 units, the volume is 27 cubic units, and the surface area is 3*3*6=54 square units.

After cutting into 27 small cubes, the side length of the cube is 1, the volume is 1 cubic unit, and the surface area is 1*1*6=6 square units.

There are 27 in total, it is easy to know, the volume remains unchanged after cutting, and the surface area is 6*27=162 square units, so it increases by 162-54=108 square units.

This topic is relatively simple, you can use the unknown, it is simpler.

Let the side length of the cube be 3cm, then the area of a face = 3cm * 3cm = 9cm 2.

Cut into 27 small squares, you need to cut 6 knives (as shown in the figure), each cut 1 knife increases the area is 2 times that of the original cube 1 face, and the surface area increases = 9 * 6 * 2 = 108 cm 2