Use Euler's Formula to find the missing number
Faces:27
Vertices:20 (1 point)
what is the number of Edges?
To find the number of edges, we can use Euler's formula which states that for any convex polyhedron, the number of faces (F), vertices (V), and edges (E) are related by the equation: F + V - E = 2.
Given that the number of faces (F) is 27 and the number of vertices (V) is 20, we can plug these values into the formula:
27 + 20 - E = 2
47 - E = 2
Now, we can solve for the number of edges (E):
E = 47 - 2
E = 45
Therefore, the missing number of edges in the polyhedron is 45.
To find the number of vertices of the gemstone, we can use Euler's formula which states that for any convex polyhedron, the number of faces (F), vertices (V), and edges (E) are related by the equation: F + V - E = 2.
Given that the number of edges (E) is 20 and the number of faces (F) is 18, we can plug these values into the formula:
18 + V - 20 = 2
V - 2 = 2
Now, we can solve for the number of vertices (V):
V = 2 + 2
V = 4
Therefore, the gemstone has 4 vertices.
Sleepy found a gemstone in the mine. It has 20 edges and 18 faces. How many vertices did the gemstone have?(1 point) Responses
12 vertices 12 vertices
4 vertices 4 vertices
34 vertices 34 vertices
10 vertices