A solid has 12 vertices and 30 edges. How many faces does not have ?

Options

A. 22
B. 24
C. 26
D. 20

Answer

To find the number of faces of a solid with 12 vertices and 30 edges, we can use Euler's formula for polyhedra, which states:

\[ V - E + F = 2 \]

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

### Step-by-Step Solution:

1. **Identify the values of vertices and edges**:
- Given \( V = 12 \) (number of vertices)
- Given \( E = 30 \) (number of edges)

2. **Substitute the values into Euler's formula**:
\[ 12 - 30 + F = 2 \]

3. **Simplify the equation**:
\[ 12 - 30 = -18 \]
So, the equation becomes:
\[ -18 + F = 2 \]

4. **Solve for \( F \)**:
To isolate \( F \), add 18 to both sides:
\[ F = 2 + 18 \]
\[ F = 20 \]

5. **Conclusion**:
The number of faces \( F \) is 20.

### Final Answer:
The solid has 20 faces.