How many faces are there in a
(i) cube, (ii) pentagonal prism, (iii) tetrahedron

Answer

To determine the number of faces in the given three-dimensional figures, we will analyze each shape step by step.

### Step-by-Step Solution:

**(i) Cube:**
1. A cube is a three-dimensional shape with all its sides equal.
2. It has six square faces.
3. Each face can be named as follows:
- Top face: A
- Bottom face: B
- Front face: C
- Back face: D
- Left face: E
- Right face: F
4. Therefore, the total number of faces in a cube is **6**.

**(ii) Pentagonal Prism:**
1. A pentagonal prism consists of two pentagonal bases and rectangular lateral faces.
2. The two pentagonal faces can be named as follows:
- Top face: A (pentagon)
- Bottom face: B (pentagon)
3. The lateral faces are rectangles. There are five lateral rectangular faces.
4. Therefore, the total number of faces in a pentagonal prism is:
- 2 (pentagonal faces) + 5 (rectangular faces) = **7**.

**(iii) Tetrahedron:**
1. A tetrahedron is a three-dimensional shape with triangular faces.
2. It has four triangular faces.
3. Each face can be named as follows:
- Face 1: A
- Face 2: B
- Face 3: C
- Face 4: D
4. Therefore, the total number of faces in a tetrahedron is **4**.

### Final Answers:
- (i) Cube: 6 faces
- (ii) Pentagonal Prism: 7 faces
- (iii) Tetrahedron: 4 faces