State whether true (T) or false (F) : A cube has 8 edges .
Text Solution
AI Generated Solution
The correct Answer is:
To determine whether the statement "A cube has 8 edges" is true or false, we can analyze the properties of a cube step by step.
### Step-by-Step Solution:
1. **Understand the Structure of a Cube**:
- A cube is a three-dimensional shape with six square faces.
2. **Identify the Components of a Cube**:
- A cube has:
- **Vertices**: Points where the edges meet.
- **Edges**: Line segments where two faces meet.
- **Faces**: The flat surfaces of the cube.
3. **Count the Edges**:
- Each face of the cube is a square, and each square has 4 edges.
- However, each edge is shared between two faces.
4. **Calculate the Total Number of Edges**:
- A cube has 6 faces, and since each edge is shared, we can count the edges:
- The edges can be counted as follows:
- 4 edges on the top face.
- 4 edges on the bottom face.
- 4 vertical edges connecting the top and bottom faces.
- Total edges = 4 (top) + 4 (bottom) + 4 (vertical) = 12 edges.
5. **Conclusion**:
- Since a cube has 12 edges, the statement "A cube has 8 edges" is **false**.
### Final Answer:
- The statement is **False (F)**.
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