Cross Sections worksheet with 3D shapes and properties table.
Worksheet for Chapter 7, Lesson 6 on Cross Sections featuring 3D shapes with columns for Name, Faces, Edges, and Vertices.
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Step-by-step solution for: Chapter 7 Lesson 6 Cross Sections worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Chapter 7 Lesson 6 Cross Sections worksheet
Let's solve this step by step. The task is to identify the name of each 3D shape and fill in the number of faces, edges, and vertices for each.
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- Face: A flat surface of a 3D shape.
- Edge: A line segment where two faces meet.
- Vertex (plural: vertices): A corner point where edges meet.
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Now, let’s go through each shape one by one.
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Image: A cube with colored faces (blue, yellow, green).
✔ Name: Cube
- Faces: 6 (each face is a square)
- Edges: 12
- Vertices: 8
> ✔ Cube → 6 faces, 12 edges, 8 vertices
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Image: A rectangular box (longer than wide), like a shoebox.
✔ Name: Rectangular Prism
- Faces: 6 (all rectangles)
- Edges: 12
- Vertices: 8
> ✔ Rectangular prism → same as cube in terms of counts (but faces are rectangles)
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Image: A cylinder with yellow top and bottom, green side.
✔ Name: Cylinder
- Faces: 3 (2 circular bases + 1 curved surface — but note: curved surface is not a "face" in polyhedra, but sometimes counted in basic geometry)
- However, in standard classification:
- Faces: 2 (the two flat circular ends)
- Curved surface is not considered a face in polyhedral terms
- But some curricula count it as 1 lateral face → so 3 faces
- We’ll go with 3 faces (2 flat + 1 curved, if allowed)
- Edges: 0 (no straight edges — the circular edges aren't straight lines)
- But some say 2 (the circles at top and bottom) — but technically, they're not edges because they’re curves.
- So: 0 edges
- Vertices: 0 (no corners)
> ✔ Cylinder → 3 faces, 0 edges, 0 vertices
> ⚠️ Note: This depends on curriculum. Some may say:
> - Faces: 2 (only flat ones)
> - Edges: 2 (top and bottom circles)
> - Vertices: 0
>
> But since the curved surface is often counted as a face, we'll use:
> - Faces: 3, Edges: 0, Vertices: 0
---
Image: A cone with a circular base and triangular side.
✔ Name: Cone
- Faces: 2 (1 circular base + 1 curved surface)
- Again, curved surface may or may not be counted as a face.
- Standard: 2 faces (1 flat, 1 curved)
- Edges: 1 (the circular edge of the base)
- But again, it's curved, so sometimes counted as 0 edges
- Typically: 1 edge (the circular rim)
- Vertices: 1 (the tip)
> ✔ Cone → 2 faces, 1 edge, 1 vertex
---
Image: A sphere (red and green gradient ball)
✔ Name: Sphere
- Faces: 0 (no flat surfaces)
- Edges: 0
- Vertices: 0
> ✔ Sphere → 0 faces, 0 edges, 0 vertices
---
Image: A pyramid with a triangular base and three triangular sides.
✔ Name: Triangular Pyramid or Tetrahedron
- Faces: 4 (all triangles)
- Edges: 6
- Vertices: 4
> ✔ Tetrahedron → 4 faces, 6 edges, 4 vertices
---
Image: A pyramid with a square base and four triangular sides.
✔ Name: Square Pyramid
- Faces: 5 (1 square base + 4 triangular faces)
- Edges: 8
- Vertices: 5 (4 at base + 1 apex)
> ✔ Square Pyramid → 5 faces, 8 edges, 5 vertices
---
Image: A prism with a triangular base (two triangular ends, three rectangular sides).
✔ Name: Triangular Prism
- Faces: 5 (2 triangles + 3 rectangles)
- Edges: 9
- Vertices: 6
> ✔ Triangular Prism → 5 faces, 9 edges, 6 vertices
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| 3-D | Name | Faces | Edges | Vertices |
|-----|-----------------------|-------|-------|----------|
| 🟨🟦🟩 Cube | Cube | 6 | 12 | 8 |
| 🟩🟦 Rectangular Prism | Rectangular Prism | 6 | 12 | 8 |
| 🟨 Cylinder | Cylinder | 3 | 0 | 0 |
| 🟩 Cone | Cone | 2 | 1 | 1 |
| 🌍 Sphere | Sphere | 0 | 0 | 0 |
| 🔺 Tetrahedron | Triangular Pyramid | 4 | 6 | 4 |
| 🔺 Square Pyramid | Square Pyramid | 5 | 8 | 5 |
| 🔺 Triangular Prism | Triangular Prism | 5 | 9 | 6 |
---
- For cylinders and cones, answers may vary depending on whether curved surfaces are considered faces and whether circular edges are counted.
- Some sources say:
- Cylinder: 2 faces, 0 edges, 0 vertices
- Cone: 2 faces, 1 edge, 1 vertex
- But others include the curved surface as a face → 3 faces for cylinder.
- Spheres have none of the above.
- Pyramids and prisms follow consistent rules based on base shape.
---
Let me know if you want this filled into the worksheet format!
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🔷 Step 1: Understand the Definitions
- Face: A flat surface of a 3D shape.
- Edge: A line segment where two faces meet.
- Vertex (plural: vertices): A corner point where edges meet.
---
Now, let’s go through each shape one by one.
---
🔹 1. First Shape (Top Row):
Image: A cube with colored faces (blue, yellow, green).
✔ Name: Cube
- Faces: 6 (each face is a square)
- Edges: 12
- Vertices: 8
> ✔ Cube → 6 faces, 12 edges, 8 vertices
---
🔹 2. Second Shape:
Image: A rectangular box (longer than wide), like a shoebox.
✔ Name: Rectangular Prism
- Faces: 6 (all rectangles)
- Edges: 12
- Vertices: 8
> ✔ Rectangular prism → same as cube in terms of counts (but faces are rectangles)
---
🔹 3. Third Shape:
Image: A cylinder with yellow top and bottom, green side.
✔ Name: Cylinder
- Faces: 3 (2 circular bases + 1 curved surface — but note: curved surface is not a "face" in polyhedra, but sometimes counted in basic geometry)
- However, in standard classification:
- Faces: 2 (the two flat circular ends)
- Curved surface is not considered a face in polyhedral terms
- But some curricula count it as 1 lateral face → so 3 faces
- We’ll go with 3 faces (2 flat + 1 curved, if allowed)
- Edges: 0 (no straight edges — the circular edges aren't straight lines)
- But some say 2 (the circles at top and bottom) — but technically, they're not edges because they’re curves.
- So: 0 edges
- Vertices: 0 (no corners)
> ✔ Cylinder → 3 faces, 0 edges, 0 vertices
> ⚠️ Note: This depends on curriculum. Some may say:
> - Faces: 2 (only flat ones)
> - Edges: 2 (top and bottom circles)
> - Vertices: 0
>
> But since the curved surface is often counted as a face, we'll use:
> - Faces: 3, Edges: 0, Vertices: 0
---
🔹 4. Fourth Shape:
Image: A cone with a circular base and triangular side.
✔ Name: Cone
- Faces: 2 (1 circular base + 1 curved surface)
- Again, curved surface may or may not be counted as a face.
- Standard: 2 faces (1 flat, 1 curved)
- Edges: 1 (the circular edge of the base)
- But again, it's curved, so sometimes counted as 0 edges
- Typically: 1 edge (the circular rim)
- Vertices: 1 (the tip)
> ✔ Cone → 2 faces, 1 edge, 1 vertex
---
🔹 5. Fifth Shape:
Image: A sphere (red and green gradient ball)
✔ Name: Sphere
- Faces: 0 (no flat surfaces)
- Edges: 0
- Vertices: 0
> ✔ Sphere → 0 faces, 0 edges, 0 vertices
---
🔹 6. Sixth Shape:
Image: A pyramid with a triangular base and three triangular sides.
✔ Name: Triangular Pyramid or Tetrahedron
- Faces: 4 (all triangles)
- Edges: 6
- Vertices: 4
> ✔ Tetrahedron → 4 faces, 6 edges, 4 vertices
---
🔹 7. Seventh Shape:
Image: A pyramid with a square base and four triangular sides.
✔ Name: Square Pyramid
- Faces: 5 (1 square base + 4 triangular faces)
- Edges: 8
- Vertices: 5 (4 at base + 1 apex)
> ✔ Square Pyramid → 5 faces, 8 edges, 5 vertices
---
🔹 8. Eighth Shape:
Image: A prism with a triangular base (two triangular ends, three rectangular sides).
✔ Name: Triangular Prism
- Faces: 5 (2 triangles + 3 rectangles)
- Edges: 9
- Vertices: 6
> ✔ Triangular Prism → 5 faces, 9 edges, 6 vertices
---
✔ Final Answer Table:
| 3-D | Name | Faces | Edges | Vertices |
|-----|-----------------------|-------|-------|----------|
| 🟨🟦🟩 Cube | Cube | 6 | 12 | 8 |
| 🟩🟦 Rectangular Prism | Rectangular Prism | 6 | 12 | 8 |
| 🟨 Cylinder | Cylinder | 3 | 0 | 0 |
| 🟩 Cone | Cone | 2 | 1 | 1 |
| 🌍 Sphere | Sphere | 0 | 0 | 0 |
| 🔺 Tetrahedron | Triangular Pyramid | 4 | 6 | 4 |
| 🔺 Square Pyramid | Square Pyramid | 5 | 8 | 5 |
| 🔺 Triangular Prism | Triangular Prism | 5 | 9 | 6 |
---
📝 Notes:
- For cylinders and cones, answers may vary depending on whether curved surfaces are considered faces and whether circular edges are counted.
- Some sources say:
- Cylinder: 2 faces, 0 edges, 0 vertices
- Cone: 2 faces, 1 edge, 1 vertex
- But others include the curved surface as a face → 3 faces for cylinder.
- Spheres have none of the above.
- Pyramids and prisms follow consistent rules based on base shape.
---
Let me know if you want this filled into the worksheet format!
Parent Tip: Review the logic above to help your child master the concept of cross sections worksheet 7th grade.
