If the number of vertices, edges and faces of a rectangular parallelopiped are denote by `v, e` and `f`respectively , the value of `(v - e + f)` is

Options

A. 0
B. 2
C. 4
D. 1

Answer

To solve the problem, we need to determine the values of the number of vertices (V), edges (E), and faces (F) of a rectangular parallelepiped.

### Step-by-Step Solution:

1. **Identify the number of vertices (V)**:
- A rectangular parallelepiped has 8 vertices. These are the corners of the shape.
- Therefore, \( V = 8 \).

2. **Identify the number of edges (E)**:
- A rectangular parallelepiped has 12 edges. These are the line segments connecting the vertices.
- Therefore, \( E = 12 \).

3. **Identify the number of faces (F)**:
- A rectangular parallelepiped has 6 faces. These are the flat surfaces that make up the shape.
- Therefore, \( F = 6 \).

4. **Substitute the values into the expression \( V - E + F \)**:
- We substitute the values we found into the expression:
\[ V - E + F = 8 - 12 + 6 \]

5. **Calculate the result**:
- First, calculate \( 8 - 12 \):
\[ 8 - 12 = -4 \]
- Then add \( 6 \):
\[ -4 + 6 = 2 \]

6. **Final result**:
- The value of \( V - E + F \) is \( 2 \).

### Conclusion:
Thus, the value of \( (V - E + F) \) for a rectangular parallelepiped is \( 2 \).