1. Use Euler’s formula to find the number of vertices in a polyhedron with 18 edges and 9 faces.

Question

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10
11
12
13

Answer 1

Euler's formula for polyhedra is given by:

\[ V - E + F = 2 \]

where \( V \) represents the number of vertices, \( E \) represents the number of edges, and \( F \) represents the number of faces.

Given:
- \( E = 18 \)
- \( F = 9 \)

We need to find \( V \). Substituting the known values into Euler's formula, we get:

\[ V - 18 + 9 = 2 \]

Simplifying the equation:

\[ V - 9 = 2 \]

Adding 9 to both sides:

\[ V = 11 \]

So, the number of vertices in the polyhedron is:

\[ \boxed{11} \]