Worksheets for learning 3D shape properties with examples and answer key.

The image you've uploaded contains a worksheet and answer key for identifying the properties of various 3D shapes, specifically focusing on the number of faces, edges, and vertices.

Let’s go through the solution step by step, explaining how to determine these properties for each shape. We'll use the answer key (top-left box) as a guide and fill in the blanks in the other tables accordingly.

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🔷 Step 1: Understand the Definitions

- Face: A flat or curved surface of a 3D shape.
- Edge: A line segment where two faces meet.
- Vertex (plural: vertices): A corner where edges meet.

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🔷 Step 2: Analyze Each Shape

We’ll go through each shape one by one and verify the properties using geometry principles.

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#### 1. Cone
- Faces: 2 (1 flat circular base + 1 curved surface)
- Edges: 1 (the circular edge of the base)
- Vertices: 1 (the tip or apex)

✔ Matches the answer key.

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#### 2. Cube
- Faces: 6 (all squares)
- Edges: 12 (each face has 4 edges, but shared)
- Vertices: 8 (corners)

✔ Correct.

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#### 3. Square-based Pyramid
- Faces: 5 (1 square base + 4 triangular sides)
- Edges: 8 (4 around base + 4 from base to apex)
- Vertices: 5 (4 at base + 1 apex)

✔ Correct.

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#### 4. Cuboid
- Faces: 6 (like cube, but rectangles)
- Edges: 12
- Vertices: 8

✔ Same as cube, just rectangular faces.

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#### 5. Cylinder
- Faces: 3 (2 flat circular bases + 1 curved surface)
- Edges: 2 (the circular edges of the top and bottom)
- Vertices: 0 (no sharp corners)

✔ Correct.

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#### 6. Sphere
- Faces: 1 (entirely curved surface – sometimes considered 1 face)
- Edges: 0
- Vertices: 0

✔ Correct.

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#### 7. Triangular Prism
- Faces: 5 (2 triangular bases + 3 rectangular sides)
- Edges: 9 (3 on each triangle + 3 connecting them)
- Vertices: 6 (3 on each triangle)

✔ Correct.

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#### 8. Tetrahedron
- Faces: 4 (all triangles)
- Edges: 6
- Vertices: 4

✔ Correct.

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🔷 Step 3: Fill in the Blank Tables

Now we can fill out the blank tables based on the above:

#### ✔ Table 1 (Top-right): "3D shape properties" (with stars)

| Shape | Faces | Edges | Vertices |
|-------------------|-------|-------|----------|
| Cone | 2 | 1 | 1 |
| Cube | 6 | 12 | 8 |
| Square-based pyramid | 5 | 8 | 5 |
| Cuboid | 6 | 12 | 8 |
| Cylinder | 3 | 2 | 0 |
| Sphere | 1 | 0 | 0 |
| Triangular Prism | 5 | 9 | 6 |
| Tetrahedron | 4 | 6 | 4 |

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#### ✔ Table 2 (Bottom-right): "Name:" with images

This table asks for:
- Name of the shape
- Faces, Edges, Vertices

We match the images:

| Image | Name | Faces | Edges | Vertices |
|-------|--------------------|-------|-------|----------|
| Blue cone | Cone | 2 | 1 | 1 |
| Yellow cube | Cube | 6 | 12 | 8 |
| Orange pyramid | Square-based pyramid | 5 | 8 | 5 |
| Pink cuboid | Cuboid | 6 | 12 | 8 |
| Green cylinder | Cylinder | 3 | 2 | 0 |
| Red sphere | Sphere | 1 | 0 | 0 |
| Blue prism | Triangular Prism | 5 | 9 | 6 |
| Green tetrahedron | Tetrahedron | 4 | 6 | 4 |

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#### ✔ Table 3 (Bottom-left): Blank grid

This is identical to the others, so we fill it in the same way.

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✔ Final Answer Summary

All 3D shapes have been correctly identified with their properties:

| Shape | Faces | Edges | Vertices |
|---------------------|-------|-------|----------|
| Cone | 2 | 1 | 1 |
| Cube | 6 | 12 | 8 |
| Square-based pyramid| 5 | 8 | 5 |
| Cuboid | 6 | 12 | 8 |
| Cylinder | 3 | 2 | 0 |
| Sphere | 1 | 0 | 0 |
| Triangular Prism | 5 | 9 | 6 |
| Tetrahedron | 4 | 6 | 4 |

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📌 Key Notes:

- Curved surfaces count as faces (e.g., cone, cylinder, sphere).
- Edges are only where two faces meet; curved surfaces don’t contribute straight edges.
- Vertices are only where edges meet (so spheres and cylinders have none).

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If this was a student worksheet, they would now be able to complete all tables using this information.

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