State whether true (T) or false (F) :
A cone has only one face .

Answer

To determine whether the statement "A cone has only one face" is true or false, we can follow these steps:

### Step 1: Understand the Structure of a Cone
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (which is circular) to a point called the apex.

**Hint:** Visualize the shape of a cone. It has a circular base and a pointed top.

### Step 2: Identify the Types of Faces on a Cone
A cone has two types of faces:
1. **Curved Face:** The surface that wraps around from the base to the apex.
2. **Circular Face:** The flat circular base at the bottom.

**Hint:** Think about the surfaces you can touch on a cone. There is one curved surface and one flat surface.

### Step 3: Count the Faces
Now, let's count the faces:
- The curved surface is one face.
- The circular base is another face.

So, a cone has a total of **two faces**.

**Hint:** When counting faces, remember to include all distinct surfaces.

### Step 4: Evaluate the Statement
The statement claims that a cone has only one face. Since we have established that a cone actually has two faces (one curved and one circular), the statement is incorrect.

**Hint:** Compare the number of faces you found with the claim made in the statement.

### Conclusion
Since a cone has two faces, the statement "A cone has only one face" is **False (F)**.

**Final Answer:** False (F)

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