A polyhedron with 8 faces and 12 vertices has .......... edges.

Options

A. 16
B. 14
C. 18
D. 10

Answer

To find the number of edges (E) in a polyhedron with 8 faces (F) and 12 vertices (V), we can use Euler's formula, which states:

\[ F + V = E + 2 \]

### Step-by-step Solution:

1. **Identify the given values**:
- Number of faces (F) = 8
- Number of vertices (V) = 12

2. **Substitute the values into Euler's formula**:
\[ F + V = E + 2 \]
Substituting the known values:
\[ 8 + 12 = E + 2 \]

3. **Simplify the left side**:
\[ 20 = E + 2 \]

4. **Isolate E**:
To find E, subtract 2 from both sides:
\[ E = 20 - 2 \]

5. **Calculate the value of E**:
\[ E = 18 \]

Thus, the polyhedron has **18 edges**.

### Final Answer:
The number of edges in the polyhedron is **18**.

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