Overview of 3D shapes with diagrams and properties such as faces, edges, and vertices.

It looks like you've uploaded a chart titled "3D Shapes" that lists various three-dimensional geometric shapes along with their properties: Faces, Edges, and Vertices. However, there are some inaccuracies in the table, particularly in the Edges and Vertices columns for certain shapes.

Let’s go through each shape and correct any errors, then explain the reasoning behind the correct values.

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🔍 Step-by-step Analysis:

#### 1. Sphere
- Diagram: Orange sphere
- Faces: 1 curved surface ✔
- Edges: 0 ✔ (No edges — smooth surface)
- Vertices: 0 ✔ (No corners)

✔ Correct

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#### 2. Hemisphere
- Diagram: Pink half-sphere
- Faces: 1 flat face + 1 curved surface ✔
- Edges: 1 ✔ (The circular edge where the flat face meets the curve)
- Vertices: 0 ✔ (No corners)

✔ Correct

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#### 3. Cone
- Diagram: Green cone
- Faces: 1 flat face (base) + 1 curved surface ✔
- Edges: 1 ✔ (The circular edge of the base)
- Vertices: 1 ✔ (The tip or apex)

✔ Correct

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#### 4. Tetrahedron (Triangular-based pyramid)
- Diagram: Blue triangular pyramid
- Faces: 4 ✔ (All triangular faces)
- Edges: 6 ✔ (Each triangle has 3 edges; shared between two faces → 4×3 / 2 = 6)
- Vertices: 4 ✔ (One at each corner)

✔ Correct

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#### 5. Square-based Pyramid
- Diagram: Purple pyramid with square base
- Faces: 5 ✔ (1 square base + 4 triangular sides)
- Edges: 8 ✔ (Base has 4 edges, 4 from base to apex)
- Vertices: 5 ✔ (4 at base, 1 apex)

✔ Correct

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#### 6. Cylinder
- Diagram: Yellow cylinder
- Faces: 2 flat faces (top and bottom) + 1 curved surface ✔
- Edges: 2 ✔ (Top and bottom circular edges)
- Vertices: 0 ✔ (No sharp corners)

✔ Correct

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#### 7. Triangular Prism
- Diagram: Purple prism
- Faces: 5 ✔ (2 triangular bases + 3 rectangular sides)
- Edges: 9 ✔ (Each triangle has 3 edges → 3×2 = 6; 3 connecting edges between bases)
- Vertices: 6 ✔ (3 on top, 3 on bottom)

✔ Correct

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#### 8. Cube
- Diagram: Green cube
- Faces: 6 ✔
- Edges: 12 ✔ (Each face has 4 edges, but shared → 6×4 / 2 = 12)
- Vertices: 8 ✔

✔ Correct

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#### 9. Cuboid
- Diagram: Orange rectangular box
- Faces: 6 ✔
- Edges: 12 ✔
- Vertices: 8 ✔

✔ Correct

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#### 10. Pentagonal Prism
- Diagram: Pink prism with pentagon bases
- Faces: 7 ✔ (2 pentagons + 5 rectangles)
- Edges: 15 ✔ (Each pentagon has 5 edges → 2×5 = 10; 5 vertical edges connecting bases → total 15)
- Vertices: 10 ✔ (5 on top, 5 on bottom)

✔ Correct

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#### 11. Hexagonal Prism
- Diagram: Teal prism with hexagon bases
- Faces: 8 ✔ (2 hexagons + 6 rectangles)
- Edges: 18 ✔ (Each hexagon has 6 edges → 2×6 = 12; 6 vertical edges → total 18)
- Vertices: 12 ✔ (6 on top, 6 on bottom)

✔ Correct

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✔ Conclusion:

All entries in the table are correct!

There are no errors in the Faces, Edges, or Vertices columns.

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📌 Summary Table (for clarity):

| Shape | Faces | Edges | Vertices |
|------------------------|-------|-------|----------|
| Sphere | 1 | 0 | 0 |
| Hemisphere | 2 | 1 | 0 |
| Cone | 2 | 1 | 1 |
| Tetrahedron | 4 | 6 | 4 |
| Square-based Pyramid | 5 | 8 | 5 |
| Cylinder | 3 | 2 | 0 |
| Triangular Prism | 5 | 9 | 6 |
| Cube | 6 | 12 | 8 |
| Cuboid | 6 | 12 | 8 |
| Pentagonal Prism | 7 | 15 | 10 |
| Hexagonal Prism | 8 | 18 | 12 |

> Note: "Faces" includes both flat and curved surfaces where applicable.

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🔎 Key Concepts:

- Face: A flat or curved surface.
- Edge: Where two faces meet (line segment).
- Vertex: A corner point where edges meet.

For prisms, the formula is:
- Faces = 2 (bases) + number of sides of base
- Edges = 3 × number of sides of base
- Vertices = 2 × number of sides of base

For pyramids:
- Faces = 1 (base) + number of sides of base
- Edges = 2 × number of sides of base
- Vertices = 1 (apex) + number of sides of base

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✔ Final Answer: The table is accurate and correctly filled out. No corrections needed.