If the number of vertices , edges and faces of a rectangular parllelopiped are denoted 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 find the values of vertices (V), edges (E), and faces (F) of a rectangular parallelepiped and then compute the expression \( V - E + F \).

### Step-by-Step Solution:

1. **Identify the number of vertices (V)**:
A rectangular parallelepiped (also known as a cuboid) has 8 vertices.
\[ V = 8 \]

**Hint**: Remember that a vertex is a corner point where edges meet. Count the corners of a cuboid.

2. **Identify the number of edges (E)**:
A rectangular parallelepiped has 12 edges.
\[ E = 12 \]

**Hint**: An edge is a line segment where two faces meet. Count the line segments connecting the vertices.

3. **Identify the number of faces (F)**:
A rectangular parallelepiped has 6 faces.
\[ F = 6 \]

**Hint**: A face is a flat surface of the solid. Count the flat surfaces that enclose the shape.

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

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

6. **Final result**:
Therefore, the value of \( V - E + F \) is:
\[ V - E + F = 2 \]

### Conclusion:
The final answer is \( 2 \).