Properties of 3D Shapes worksheet with illustrations and questions for identifying geometric figures.
Worksheet titled "Properties of 3D Shapes" featuring nine 3D shapes with spaces to name them and identify their vertices, faces, and edges. Includes an extension section with clues about prisms and pyramids.
JPG
1241×1754
459.2 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #770485
⭐
Show Answer Key & Explanations
Step-by-step solution for: Properties of 3D Shapes | PDF printable Geometry Worksheets
▼
Show Answer Key & Explanations
Step-by-step solution for: Properties of 3D Shapes | PDF printable Geometry Worksheets
Let’s go step by step to fill in the properties of each 3D shape. We’ll name each shape, then count its vertices (corners), faces (flat or curved surfaces), and edges (lines where two faces meet).
---
1) Rectangular Prism (or Cuboid)
- Vertices: 8 corners
- Faces: 6 flat rectangles
- Edges: 12 lines
✔ Name: Rectangular Prism
Vertices: 8
Faces: 6
Edges: 12
---
2) Triangular Prism
- Has 2 triangular bases + 3 rectangular sides → total 5 faces
- Vertices: 3 on top triangle + 3 on bottom = 6
- Edges: 3 on top + 3 on bottom + 3 connecting them = 9
✔ Name: Triangular Prism
Vertices: 6
Faces: 5
Edges: 9
---
3) Cone
- Point at top (apex) + circular base
- Vertices: 1 (the apex — some curricula say 0 for cones since it’s not a “corner” like polyhedra, but many school worksheets count the apex as 1 vertex)
→ *Note: In most elementary/middle school contexts, cone has 1 vertex.*
- Faces: 1 flat circle + 1 curved surface = 2 faces
- Edges: 1 (where the curved surface meets the base)
✔ Name: Cone
Vertices: 1
Faces: 2
Edges: 1
*(Some systems say 0 vertices for cone — but given this worksheet includes pyramids with apex counted, we’ll use 1.)*
---
4) Square Pyramid
- Base is square (4 vertices), plus 1 apex → total 5 vertices
- Faces: 4 triangles + 1 square = 5 faces
- Edges: 4 around base + 4 from base to apex = 8 edges
✔ Name: Square Pyramid
Vertices: 5
Faces: 5
Edges: 8
---
5) Cylinder
- Two flat circles + one curved surface
- Vertices: 0 (no corners)
- Faces: 3? Wait — actually, in standard geometry for kids:
→ Usually taught as: 2 flat faces (top and bottom) + 1 curved face = 3 faces?
BUT — many curricula (especially US Common Core aligned) consider cylinder to have 2 faces (only the flat ones) and ignore the curved surface as a “face” for counting purposes?
Wait — let’s check consistency.
Actually, looking at common school standards (like Cazoom Maths):
Cylinder:
- Vertices: 0
- Faces: 2 (the two flat circular ends) — sometimes they include curved surface as 1 face → total 3?
But in many worksheets like this, they treat curved surfaces as faces too.
Let me double-check with known answers for similar worksheets:
Standard answer for cylinder in such sheets:
- Vertices: 0
- Faces: 3 (2 flat + 1 curved)
- Edges: 2 (the two circular rims)
Yes — that’s consistent.
✔ Name: Cylinder
Vertices: 0
Faces: 3
Edges: 2
---
6) Cube
Special case of rectangular prism — all faces squares.
Same counts:
- Vertices: 8
- Faces: 6
- Edges: 12
✔ Name: Cube
Vertices: 8
Faces: 6
Edges: 12
---
7) Sphere
Perfectly round ball.
- No vertices, no edges, only 1 continuous curved surface.
In school math:
- Vertices: 0
- Faces: 1 (curved surface)
- Edges: 0
✔ Name: Sphere
Vertices: 0
Faces: 1
Edges: 0
---
8) Octahedron (looks like two pyramids stuck together at base)
It’s a Platonic solid.
- Vertices: 6 (top, bottom, and 4 around middle)
- Faces: 8 triangles
- Edges: 12
You can think: 4 edges around equator + 4 up to top + 4 down to bottom = 12
Vertices: 4 around middle + top + bottom = 6
Faces: 8 triangles (4 upper, 4 lower)
✔ Name: Octahedron
Vertices: 6
Faces: 8
Edges: 12
---
9) Pentagonal Prism
Base is pentagon (5-gon).
- Vertices: 5 on top + 5 on bottom = 10
- Faces: 2 pentagons + 5 rectangles = 7 faces
- Edges: 5 top + 5 bottom + 5 vertical = 15 edges
✔ Name: Pentagonal Prism
Vertices: 10
Faces: 7
Edges: 15
---
Now Extension Section:
We’re told: Shapes A and B are prisms, C is a pyramid.
Use Euler’s formula for polyhedra: V - E + F = 2 (for convex polyhedra without holes)
Check if numbers fit.
---
A) Vertices: 12, Faces: 8, Edges: 18
V - E + F = 12 - 18 + 8 = 2 → OK.
Prism with n-gon base has:
- Vertices: 2n
- Faces: n + 2
- Edges: 3n
So set 2n = 12 → n = 6 → Hexagonal Prism
Check: Faces = 6 + 2 = 8 ✔️
Edges = 3×6 = 18 ✔️
✔ A) Hexagonal Prism
---
B) Vertices: 16, Faces: 10, Edges: 24
V - E + F = 16 - 24 + 10 = 2 → OK.
Prism: 2n = 16 → n = 8 → Octagonal Prism
Faces: 8 + 2 = 10 ✔️
Edges: 3×8 = 24 ✔️
✔ B) Octagonal Prism
---
C) Vertices: 6, Faces: 6, Edges: 10
Pyramid with n-gon base has:
- Vertices: n + 1
- Faces: n + 1
- Edges: 2n
Set n + 1 = 6 → n = 5 → Pentagonal Pyramid
Check: Faces = 5 + 1 = 6 ✔️
Edges = 2×5 = 10 ✔️
✔ C) Pentagonal Pyramid
---
Final Answer:
1) Name: Rectangular Prism
Vertices: 8
Faces: 6
Edges: 12
2) Name: Triangular Prism
Vertices: 6
Faces: 5
Edges: 9
3) Name: Cone
Vertices: 1
Faces: 2
Edges: 1
4) Name: Square Pyramid
Vertices: 5
Faces: 5
Edges: 8
5) Name: Cylinder
Vertices: 0
Faces: 3
Edges: 2
6) Name: Cube
Vertices: 8
Faces: 6
Edges: 12
7) Name: Sphere
Vertices: 0
Faces: 1
Edges: 0
8) Name: Octahedron
Vertices: 6
Faces: 8
Edges: 12
9) Name: Pentagonal Prism
Vertices: 10
Faces: 7
Edges: 15
Extension:
A) Name: Hexagonal Prism
Vertices: 12
Faces: 8
Edges: 18
B) Name: Octagonal Prism
Vertices: 16
Faces: 10
Edges: 24
C) Name: Pentagonal Pyramid
Vertices: 6
Faces: 6
Edges: 10
---
1) Rectangular Prism (or Cuboid)
- Vertices: 8 corners
- Faces: 6 flat rectangles
- Edges: 12 lines
✔ Name: Rectangular Prism
Vertices: 8
Faces: 6
Edges: 12
---
2) Triangular Prism
- Has 2 triangular bases + 3 rectangular sides → total 5 faces
- Vertices: 3 on top triangle + 3 on bottom = 6
- Edges: 3 on top + 3 on bottom + 3 connecting them = 9
✔ Name: Triangular Prism
Vertices: 6
Faces: 5
Edges: 9
---
3) Cone
- Point at top (apex) + circular base
- Vertices: 1 (the apex — some curricula say 0 for cones since it’s not a “corner” like polyhedra, but many school worksheets count the apex as 1 vertex)
→ *Note: In most elementary/middle school contexts, cone has 1 vertex.*
- Faces: 1 flat circle + 1 curved surface = 2 faces
- Edges: 1 (where the curved surface meets the base)
✔ Name: Cone
Vertices: 1
Faces: 2
Edges: 1
*(Some systems say 0 vertices for cone — but given this worksheet includes pyramids with apex counted, we’ll use 1.)*
---
4) Square Pyramid
- Base is square (4 vertices), plus 1 apex → total 5 vertices
- Faces: 4 triangles + 1 square = 5 faces
- Edges: 4 around base + 4 from base to apex = 8 edges
✔ Name: Square Pyramid
Vertices: 5
Faces: 5
Edges: 8
---
5) Cylinder
- Two flat circles + one curved surface
- Vertices: 0 (no corners)
- Faces: 3? Wait — actually, in standard geometry for kids:
→ Usually taught as: 2 flat faces (top and bottom) + 1 curved face = 3 faces?
BUT — many curricula (especially US Common Core aligned) consider cylinder to have 2 faces (only the flat ones) and ignore the curved surface as a “face” for counting purposes?
Wait — let’s check consistency.
Actually, looking at common school standards (like Cazoom Maths):
Cylinder:
- Vertices: 0
- Faces: 2 (the two flat circular ends) — sometimes they include curved surface as 1 face → total 3?
But in many worksheets like this, they treat curved surfaces as faces too.
Let me double-check with known answers for similar worksheets:
Standard answer for cylinder in such sheets:
- Vertices: 0
- Faces: 3 (2 flat + 1 curved)
- Edges: 2 (the two circular rims)
Yes — that’s consistent.
✔ Name: Cylinder
Vertices: 0
Faces: 3
Edges: 2
---
6) Cube
Special case of rectangular prism — all faces squares.
Same counts:
- Vertices: 8
- Faces: 6
- Edges: 12
✔ Name: Cube
Vertices: 8
Faces: 6
Edges: 12
---
7) Sphere
Perfectly round ball.
- No vertices, no edges, only 1 continuous curved surface.
In school math:
- Vertices: 0
- Faces: 1 (curved surface)
- Edges: 0
✔ Name: Sphere
Vertices: 0
Faces: 1
Edges: 0
---
8) Octahedron (looks like two pyramids stuck together at base)
It’s a Platonic solid.
- Vertices: 6 (top, bottom, and 4 around middle)
- Faces: 8 triangles
- Edges: 12
You can think: 4 edges around equator + 4 up to top + 4 down to bottom = 12
Vertices: 4 around middle + top + bottom = 6
Faces: 8 triangles (4 upper, 4 lower)
✔ Name: Octahedron
Vertices: 6
Faces: 8
Edges: 12
---
9) Pentagonal Prism
Base is pentagon (5-gon).
- Vertices: 5 on top + 5 on bottom = 10
- Faces: 2 pentagons + 5 rectangles = 7 faces
- Edges: 5 top + 5 bottom + 5 vertical = 15 edges
✔ Name: Pentagonal Prism
Vertices: 10
Faces: 7
Edges: 15
---
Now Extension Section:
We’re told: Shapes A and B are prisms, C is a pyramid.
Use Euler’s formula for polyhedra: V - E + F = 2 (for convex polyhedra without holes)
Check if numbers fit.
---
A) Vertices: 12, Faces: 8, Edges: 18
V - E + F = 12 - 18 + 8 = 2 → OK.
Prism with n-gon base has:
- Vertices: 2n
- Faces: n + 2
- Edges: 3n
So set 2n = 12 → n = 6 → Hexagonal Prism
Check: Faces = 6 + 2 = 8 ✔️
Edges = 3×6 = 18 ✔️
✔ A) Hexagonal Prism
---
B) Vertices: 16, Faces: 10, Edges: 24
V - E + F = 16 - 24 + 10 = 2 → OK.
Prism: 2n = 16 → n = 8 → Octagonal Prism
Faces: 8 + 2 = 10 ✔️
Edges: 3×8 = 24 ✔️
✔ B) Octagonal Prism
---
C) Vertices: 6, Faces: 6, Edges: 10
Pyramid with n-gon base has:
- Vertices: n + 1
- Faces: n + 1
- Edges: 2n
Set n + 1 = 6 → n = 5 → Pentagonal Pyramid
Check: Faces = 5 + 1 = 6 ✔️
Edges = 2×5 = 10 ✔️
✔ C) Pentagonal Pyramid
---
Final Answer:
1) Name: Rectangular Prism
Vertices: 8
Faces: 6
Edges: 12
2) Name: Triangular Prism
Vertices: 6
Faces: 5
Edges: 9
3) Name: Cone
Vertices: 1
Faces: 2
Edges: 1
4) Name: Square Pyramid
Vertices: 5
Faces: 5
Edges: 8
5) Name: Cylinder
Vertices: 0
Faces: 3
Edges: 2
6) Name: Cube
Vertices: 8
Faces: 6
Edges: 12
7) Name: Sphere
Vertices: 0
Faces: 1
Edges: 0
8) Name: Octahedron
Vertices: 6
Faces: 8
Edges: 12
9) Name: Pentagonal Prism
Vertices: 10
Faces: 7
Edges: 15
Extension:
A) Name: Hexagonal Prism
Vertices: 12
Faces: 8
Edges: 18
B) Name: Octagonal Prism
Vertices: 16
Faces: 10
Edges: 24
C) Name: Pentagonal Pyramid
Vertices: 6
Faces: 6
Edges: 10
Parent Tip: Review the logic above to help your child master the concept of 3d geometry worksheet.
