A polyhedron has 11 faces and 18 vertices. Find the number of edges.

Options

A. 15
B. 27
C. 33
D. 21

Answer

To solve the problem of finding the number of edges in a polyhedron with 11 faces and 18 vertices, we can use Euler's formula for polyhedra. Euler's formula states that:

\[ V - E + F = 2 \]

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

Given:
- \( F = 11 \) (the number of faces)
- \( V = 18 \) (the number of vertices)

We need to find \( E \) (the number of edges).

### Step 1: Substitute the known values into Euler's formula.

Using the formula:

\[ V - E + F = 2 \]

Substituting the known values:

\[ 18 - E + 11 = 2 \]

### Step 2: Simplify the equation.

Combine the constants on the left side:

\[ 29 - E = 2 \]

### Step 3: Solve for \( E \).

Rearranging the equation to isolate \( E \):

\[ -E = 2 - 29 \]

\[ -E = -27 \]

Multiplying both sides by -1 gives:

\[ E = 27 \]

### Conclusion:

The number of edges \( E \) in the polyhedron is **27**.