Question

The equation v+f-2=e relates the number of vertices, faces, and edges in a Platonic solid. Write an equation that makes it easier to find the number of vertices in a Dodecahedron, which has 30 edges.

A) v+12-2=30
B) v+12-2=20
C) v+12-2=10
D) v+12-2=40

Answer 1

The number of vertices in a Dodecahedron with 30 edges is 40.

Step-by-step explanation:

The equation v+f-2=e relates the number of vertices, faces, and edges in a Platonic solid. To find the number of vertices in a Dodecahedron with 30 edges, we can rearrange the equation to solve for v. Adding 2 to both sides of the equation, we get v = e+f-2. Substituting the given values for a Dodecahedron, we have v = 30+12-2 = 40.