If the vertices and faces of a solid are 34 and 18 respectively, then find the number of edges of the solid.

Options

A. 48
B. 50
C. 52
D. 46

Answer

To solve the problem, we will use Euler's formula for polyhedra, which states:

\[ F + V = E + 2 \]

where:
- \( F \) = number of faces
- \( V \) = number of vertices
- \( E \) = number of edges

Given:
- Number of vertices \( V = 34 \)
- Number of faces \( F = 18 \)

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

### Step-by-Step Solution:

1. **Write down Euler's formula**:
\[ F + V = E + 2 \]

2. **Substitute the known values into the formula**:
- Substitute \( F = 18 \) and \( V = 34 \):
\[ 18 + 34 = E + 2 \]

3. **Calculate the left-hand side**:
- Add \( 18 \) and \( 34 \):
\[ 52 = E + 2 \]

4. **Isolate \( E \)**:
- To find \( E \), subtract \( 2 \) from both sides:
\[ E = 52 - 2 \]

5. **Calculate the value of \( E \)**:
\[ E = 50 \]

### Final Answer:
The number of edges \( E \) of the solid is \( 50 \).

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