3D Shape Properties Worksheet - Identify and count faces, edges, and vertices of common 3D shapes.

Let's solve the 3D Shape Properties Sheet 5 step by step. We'll identify each shape, and then fill in the number of faces, edges, and vertices for each.

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🔹 1. First Shape (Top Left)

- Shape: Cube
- Faces: 6 (all squares)
- Edges: 12
- Vertices: 8

✔ Answer:
- Name: Cube
- Faces: 6
- Edges: 12
- Vertices: 8

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🔹 2. Second Shape (Top Right)

- Shape: Triangular Prism
- Faces: 5 (2 triangular bases + 3 rectangular sides)
- Edges: 9
- Vertices: 6

✔ Answer:
- Name: Triangular prism
- Faces: 5
- Edges: 9
- Vertices: 6

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🔹 3. Third Shape (Middle Left)

- Shape: Triangular Pyramid (Tetrahedron)
- Faces: 4 (all triangles)
- Edges: 6
- Vertices: 4

✔ Answer:
- Name: Triangular pyramid
- Faces: 4
- Edges: 6
- Vertices: 4

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🔹 4. Fourth Shape (Middle Right)

- Shape: Cuboid (Rectangular Prism)
- Faces: 6 (all rectangles)
- Edges: 12
- Vertices: 8

✔ Answer:
- Name: Cuboid
- Faces: 6
- Edges: 12
- Vertices: 8

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🔹 5. Fifth Shape (Bottom Left, Row 3)

- Shape: Cone
- Faces: 2 (1 circular base + 1 curved surface — but note: in some definitions, curved surfaces aren't counted as "faces" in polyhedra; however, here we count it as 1 face if only flat surfaces are considered. But since the cone has a curved surface and a base, and the base is a face, we say:
- Faces: 2 (1 flat, 1 curved — though curved is not a polygonal face)
- However, in many elementary contexts, the curved surface is not counted as a face, so:
- Faces: 1 (only the base)
- But typically, a cone has 2 faces: one flat circular base and one curved surface.
- But strictly speaking, faces are flat surfaces, so only the base counts as a face → 1 face
- Edges: 1 (the circular edge of the base)
- Vertices: 1 (the tip)

But let’s clarify:

In standard elementary geometry:
- Cone:
- Faces: 2 (1 flat base + 1 curved surface — sometimes curved is not counted)
- But since faces are usually flat polygons, curved surfaces are not counted as faces.
- So:
- Faces: 1 (base)
- Edges: 1 (the circular edge)
- Vertices: 1 (apex)

However, some sources define:
- Faces: 2 (including curved surface)
- But for consistency with polyhedra (which have only flat faces), we go with:
- Faces: 1
- Edges: 1 (circular edge)
- Vertices: 1

But in this worksheet, they likely expect:
- Faces: 2 (including curved surface)
- Edges: 1
- Vertices: 1

But wait — edges are where two faces meet. Since the curved surface meets the base along a curve, that's 1 edge (a circle).

So:
- Name: Cone
- Faces: 2 (1 flat, 1 curved)
- Edges: 1
- Vertices: 1

✔ Answer:
- Name: Cone
- Faces: 2
- Edges: 1
- Vertices: 1

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🔹 6. Sixth Shape (Middle Right, Row 3)

- Shape: Cylinder
- Faces: 3 (2 circular bases + 1 curved surface)
- But again, faces are flat → so only 2 flat faces (top and bottom)
- Curved surface is not a face
- So:
- Faces: 2
- Edges: 2 (top and bottom circles)
- Vertices: 0 (no sharp corners)

But in some curricula:
- Faces: 3 (counting curved surface)
- But again, faces = flat surfaces → only 2

So:
- Faces: 2
- Edges: 2
- Vertices: 0

✔ Answer:
- Name: Cylinder
- Faces: 2
- Edges: 2
- Vertices: 0

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🔹 7. Seventh Shape (Bottom Left)

- Shape: Sphere
- Faces: 0 (no flat surfaces)
- Edges: 0
- Vertices: 0

✔ Answer:
- Name: Sphere
- Faces: 0
- Edges: 0
- Vertices: 0

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🔹 8. Eighth Shape (Bottom Right)

- Shape: Square Pyramid
- Faces: 5 (1 square base + 4 triangular sides)
- Edges: 8
- Vertices: 5 (4 at base + 1 apex)

✔ Answer:
- Name: Square pyramid
- Faces: 5
- Edges: 8
- Vertices: 5

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## ✔ Final Answer Table:

| Shape | Name | Faces | Edges | Vertices |
|--------------------|------------------|-------|-------|----------|
| 1 | Cube | 6 | 12 | 8 |
| 2 | Triangular prism | 5 | 9 | 6 |
| 3 | Triangular pyramid | 4 | 6 | 4 |
| 4 | Cuboid | 6 | 12 | 8 |
| 5 | Cone | 2 | 1 | 1 |
| 6 | Cylinder | 2 | 2 | 0 |
| 7 | Sphere | 0 | 0 | 0 |
| 8 | Square pyramid | 5 | 8 | 5 |

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📝 Notes:

- Face: A flat surface (polygon). Curved surfaces (like on cones and cylinders) are not counted as faces in this context unless specified.
- Edge: Where two faces meet (line segment).
- Vertex: A corner point where edges meet.
- Cone & Cylinder: These have curved surfaces, so their properties differ from polyhedra.

This worksheet uses common elementary school conventions, so:
- Cone: 2 faces (1 flat base, 1 curved), 1 edge (circle), 1 vertex (tip)
- Cylinder: 2 faces (top and bottom), 2 edges (top and bottom circles), 0 vertices
- Sphere: 0 faces, edges, vertices

✔ All answers match standard expectations for this level.

Let me know if you'd like a printable version or explanation for any specific shape!