Given that the edge length of a cube is 8 cm, make another cube so that its volume is three times the volume of the original cube, and calculate the surface area of the cube (accurate to 0.1 square centimeter)

Given that the edge length of a cube is 8 cm, make another cube so that its volume is three times the volume of the original cube, and calculate the surface area of the cube (accurate to 0.1 square centimeter)

Let the new side length of the cube be X
So x ^ 3 = 8 ^ 3 × 3
Then x = 8 × 3 ^ (1 / 3)
The surface area is 6 × x ^ 2 = 6 × 64 × 3 ^ (2 / 3) square cm ≈ 798.8 square cm

How many cubes can you cut from a cube with an edge length of 6cm into a cube with an edge length of 2cm? How many square centimeters has the surface area increased?

6÷2=3
3 × 3 × 3 = 27
It can cut 27
Surface area increase = 27 × 6 × 2 × 2-6 × 6 × 6 = 432 square centimeter

The total surface area of these small cubes is larger than that of the original cubes

The cube with an edge length of 6 cm has a volume of 6 * 6 * 6 = 216 cubic cm
The cube whose edge length is 2 cm has a volume of 2 * 2 * 2 = 8 cubic cm
It can be cut into 216 / 8 = 27
The cube with the edge length of 6 cm has a surface area of 6 * 6 * 6 = 216 square cm
The cube with the edge length of 2 cm has a surface area of 2 * 2 * 6 = 24 square cm
The surface area increased by 24 * 27-216 = 432 square centimeters

After eight small cubes with the edge length of 1cm are put together into a large cube, the edge length of the large cube is () cm, the surface area is () cm, and the volume is () cm

After 8 small cubes with edge length of 1cm are put together into a large cube, the edge length of the large cube is (2) cm, the surface area is 24 square cm, and the volume is (8 cubic cm). Because there are 8 cubes, they can only be put together into a cube with edge length of 2cm, and the square with surface area equal to six times the edge length = 6 * 2 * 2 = 24 square cm

In the middle of a large cube, dig out a small cube whose edge length is 1cm. Does the surface area of the large cube increase or decrease?
How many square centimeters does it increase or decrease?

In the middle of a large cube, a small cube with an edge length of 1cm is excavated, and the surface area of the large cube is increased by 4cm

The ratio of the edge length of the two cubes is 2:1, the sum of the volumes is 27 cubic centimeters, and the volume of the large square is () cubic centimeters

The ratio of edge length and volume is 2:1 and 8:1, respectively
The volume of a large square is 27 / (8 + 1) * 8 = 24 cubic centimeters

After a polygon cuts off an angle, the sum of the inner angles of the formed polygon is 720 degrees

After subtracting one angle, there are three possible cases
1. 1 less than the original number of edges
2. Equal to the original number of edges
3. 1 more than the original number of edges [without vertex clipping]
I believe you can draw specific graphics
Let the original number of edges be n
（1）【（n-1）-2】180°=720°
The solution is n = 7
（2）（n-2）180°=720°
The solution is n = 6
（3）【（n+1）-2】180°=720°
The solution is n = 5
So: the number of sides of the original polygon is 5 or 6 or 7

After a polygon cuts off an angle, the sum of the inner angles of the new polygon is 2520 degrees

Let the number of sides of the new polygon be n, then (n-2) · 180 ° = 2520 ° and the solution is n = 16. ① if the number of sides after cutting off a corner increases by 1, then the number of sides of the original polygon is 15. ② if the number of sides after cutting off a corner remains unchanged, then the number of sides of the original polygon is 16. ③ if the number of sides after cutting off a corner decreases by 1, then the number of sides of the original polygon is 17, so the number of sides of the polygon can be 15, 16 or 17 , 16 or 17

Make a straight line through a vertex of a polygon, cut off two corners of the polygon, and the sum of its inner angles becomes 1260 degrees, then the original number of sides of the polygon is 1260 degrees______ ．

Because 1260 = 7 × 180, it is now a 7 + 2 = 9 polygon. A vertex of a polygon makes a straight line and cuts off two corners of the polygon. There are two cases: first, if the line passes through another vertex, three edges are reduced and one edge is added. In total, two edges are reduced, and the original is 9 + 2 = 11; second, if the line does not pass through other vertices, only two edges are reduced The other one is just a little shorter, but it's still an edge. Add another edge to reduce one edge. The original number is 9 + 1 = 10. In conclusion, the original number of edges is 11 or 10, so fill in: 10 or 11

Make a straight line through a vertex of a polygon, cut off two corners of the polygon, and the sum of its inner angles becomes 1260 degrees, then the original number of sides of the polygon is 1260 degrees______ ．

Because 1260 = 7 × 180, it is now a 7 + 2 = 9 polygon. A vertex of a polygon makes a straight line and cuts off two corners of the polygon. There are two cases: first, if the line passes through another vertex, three sides are reduced and one side is added. In total, two sides are reduced, which turned out to be 9 + 2 = 11