The surface area of a cube is a ^ 2, its vertices are on the ball, and the surface area of the ball is

The surface area of a cube is a ^ 2, its vertices are on the ball, and the surface area of the ball is

The answer is very correct. I'll add a picture to help him explain, which will make it easier for you to understand
The left figure is a cube and its circumscribed sphere. Assuming that the edge length of the cube is l, the above diagonal length is (√ 2) l according to the Pythagorean theorem;
We cut the ball along the upper and lower diagonals and get the right figure
            (2r)^2=L^2+【(√2)L】^2=3L^2
Then substitute the previous L ^ 2 = a ^ 2 / 6 into the above formula, and you can get R ^ 2 = a ^ 2 / 8
Then calculate the surface area of the ball: S = 4 π R ^ 2 = π a ^ 2 / 2

If a polyhedron has 9 vertices and 16 edges, the number of faces is? A: 7 B: 8 C: 9 D: 10

Vertex number + face number = edge number + 2
9 + number of faces = 16 + 2
C：9

If a polyhedron has 9 edges and 6 vertices, what is the number of faces

5 sides
Number of faces - number of edges + number of vertices = 2

What is the number of faces of a polyhedron with 9 edges and 6 vertices

Five faces, such as triangular prism, triangular pyramid

If the number of faces of a polyhedron is 8 larger than the number of vertices and has 30 edges, then the number of faces of the polyhedron is?

Polyhedron, face number f, vertex number V, edge number E
V+F-E=2
The number of faces is 8 larger than the number of vertices, so v = F-8
E=30
F-8+F-30=2
Solve the equation f = 20
That is, the number of faces is 20

For a polyhedron with 5 vertices and 5 faces, the number of edges is?
Number of edges?

Pyramid, 8-sided

The relationship among the number of vertices, edges and faces of each polyhedron is

As far as I know: the number of faces (f) + the number of vertices (V) - the number of edges (E) = 2!

The number of faces and vertices of a polyhedron is equal, and it has 12 edges. How many faces is the polyhedron

Using Euler formula: number of faces + number of vertices = number of edges + 2
Let the number of faces = the number of vertices = x, then 2x = 12 + 2, x = 7
It's a heptahedron

If the number of faces of a prism is 12 and the number of edges is 30, then the number of vertices of the prism is 12______ ．

∵ the relationship among vertex number V, face number f and edge number e of a simple polyhedron is: V + F-E = 2, the face number of a prism is 12, and the edge number is 30, then the vertex number is: V + 12-30 = 2, and the solution is: v = 2. So the answer is: 20

Laiwu is rich in ginger. Last year, a production cooperative harvested 200 tons of ginger, and planned to sell it by wholesale and retail. According to the market survey, 6 tons of ginger were sold in wholesale every day. (1) affected by the weather, site and other factors, the sales task should be completed ahead of time. Under the condition that the average daily wholesale volume remained unchanged, the actual average daily retail volume increased by 2 tons compared with the original plan, As a result, the sales task was completed five days ahead of schedule. How many tons of retail products were sold per day? (2) Under the condition of (1), if the wholesale profit is 2000 yuan per ton and the retail profit is 2200 yuan per ton, the actual total profit is calculated

According to the meaning of the question, we get 2006 + X − 2006 + (x + 2) = 5, sorting out, we get x2 + 14x-32 = 0, and the solution is X1 = 2, X2 = - 16. After testing, x = 2 is the root of the original equation, x = - 16 does not conform to the meaning of the question, so we give up