Find the correct 3D shape based on the number of faces, edges, and corners in this educational worksheet.

Let's solve the worksheet step by step. The goal is to match each description (number of faces, edges, and corners) with the correct 3D shape from the options provided.

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🔍 Key Definitions:

- Face: A flat surface of a 3D shape.
- Edge: A line segment where two faces meet.
- Corner (Vertex): A point where edges meet.

We’ll go through each question one by one.

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1) Faces: 5, Edges: 8, Corners: 5

Look at the options:

- a) Cube → 6 faces, 12 edges, 8 corners ✘
- b) Cone → 2 faces (1 curved, 1 base), 1 edge, 1 corner ✘
- c) Square pyramid → 5 faces (4 triangular + 1 square base), 8 edges, 5 corners ✔

✔ Answer: c)

> ✔️ A square pyramid has:
> - 5 faces (1 square base + 4 triangles),
> - 8 edges (4 around base, 4 from apex),
> - 5 vertices (4 base corners + 1 apex).

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2) Faces: 6, Edges: 12, Corners: 8

Options:

- a) Triangular pyramid (tetrahedron) → 4 faces, 6 edges, 4 corners ✘
- b) Rectangular prism (cuboid) → 6 faces, 12 edges, 8 corners ✔
- c) Sphere → 0 faces, 0 edges, 0 corners ✘

✔ Answer: b)

> ✔️ A rectangular prism (like a box) has:
> - 6 rectangular faces,
> - 12 edges,
> - 8 corners.

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3) Faces: 4, Edges: 6, Corners: 4

Options:

- a) Triangular prism → 5 faces, 9 edges, 6 corners ✘
- b) Cube → 6 faces, 12 edges, 8 corners ✘
- c) Tetrahedron (triangular pyramid) → 4 triangular faces, 6 edges, 4 corners ✔

✔ Answer: c)

> ✔️ A tetrahedron is a pyramid with a triangular base and 3 triangular sides — total 4 faces.

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4) Faces: 5, Edges: 9, Corners: 6

Options:

- a) Cylinder → 3 faces (2 circular bases + 1 curved surface), 2 edges (circular), 0 corners ✘
- b) Triangular prism → 5 faces (2 triangular bases + 3 rectangles), 9 edges, 6 corners ✔
- c) Cube → 6 faces, 12 edges, 8 corners ✘

✔ Answer: b)

> ✔️ Triangular prism:
> - 2 triangular bases → 2 faces,
> - 3 rectangular sides → 3 faces → total 5 faces,
> - Each triangle has 3 edges, but shared → 3 + 3 + 3 = 9 edges,
> - 6 vertices (3 on top, 3 on bottom).

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5) Faces: 6, Edges: 12, Corners: 8

This is the same as Question 2!

Options:

- a) Cube → 6 faces, 12 edges, 8 corners ✔
- b) Cone → 2 faces, 1 edge, 1 corner ✘
- c) Tetrahedron → 4 faces, 6 edges, 4 corners ✘

✔ Answer: a)

> ✔️ Cube has:
> - 6 square faces,
> - 12 edges,
> - 8 corners.

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✔ Final Answers:

| Question | Correct Option |
|--------|----------------|
| 1 | c |
| 2 | b |
| 3 | c |
| 4 | b |
| 5 | a |

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📝 Summary:

- Use known properties of common 3D shapes.
- Count carefully: faces, edges, vertices.
- Remember: Cone and cylinder have curved surfaces and are not polyhedra (so they don’t follow Euler’s formula in the same way).
- Pyramids and prisms are key here.

Let me know if you'd like a printable version or explanation with diagrams!