🧊 3D Shapes — Grade 5

Discover 3D shapes — count faces, vertices and edges, and explore nets and cross-sections!

1. 3D Shape Names

Cube

6 square faces — dice

Cuboid

6 rectangle faces — cereal box

Cylinder

2 circles + 1 curved surface — tin can

Cone

1 circle + 1 curved surface — ice cream cone

Sphere

1 curved surface — football

Triangular Prism

2 triangles + 3 rectangles — tent

Square Pyramid

1 square + 4 triangles — Egyptian pyramid

Tetrahedron

4 triangular faces — D4 dice

2. Faces, Edges and Vertices

Face = a flat surface. Edge = where two faces meet. Vertex = a corner point.

Shape	Faces (F)	Vertices (V)	Edges (E)
Cube	6	8	12
Cuboid	6	8	12
Triangular Prism	5	6	9
Square Pyramid	5	5	8
Tetrahedron	4	4	6
Cylinder	3	0	2
Cone	2	1	1
Sphere	1	0	0

Euler's Formula: For all polyhedra: F + V − E = 2

Cube: 6 + 8 − 12 = 2 ✓

3. Prisms and Pyramids

A prism has the same cross-section all the way through. Its two end faces are identical polygons.

A pyramid comes to a point (apex) at the top. The base is a polygon.

A triangular prism: end faces are triangles. It has 5 faces, 6 vertices, 9 edges.

A square pyramid: base is a square. It has 5 faces, 5 vertices, 8 edges.

4. Nets

A net is a flat shape that can be folded to make a 3D shape. The number of shapes in a net equals the number of faces.

A cube has 6 faces, so its net has 6 squares.

A triangular prism has 5 faces: 2 triangles + 3 rectangles.

5. Cross-Sections

A cross-section is the shape you get when you slice through a 3D shape.

Sphere

Always a circle

Cube

Square (or rectangle)

Cylinder

Circle (horizontal) or Rectangle (vertical)

Triangular Prism

Triangle

Square Pyramid

Square (at base) or Triangle (vertical)

🧊 Worked Examples

Example 1 — F, V, E

How many edges does a triangular prism have?

Triangular prism: 5 faces, 6 vertices, 9 edges

Example 2 — Euler's Formula

A polyhedron has 6 faces and 12 edges. How many vertices?

F + V − E = 2 → 6 + V − 12 = 2 → V = 8

Example 3 — Net Faces

The net of a square pyramid has how many shapes?

Square pyramid: 5 faces, so its net has 5 shapes (1 square + 4 triangles).

Example 4 — Identify Shape

A solid has F=5, V=5, E=8. What shape is it?

5 + 5 − 8 = 2 ✓ and F=5, V=5, E=8 → Square Pyramid (code 2)

Example 5 — Cross-Section

What cross-section do you get slicing a cylinder horizontally?

A horizontal slice of a cylinder = Circle (code 1)

🔭 3D Shape Explorer

Shape Properties

Choose shape

Euler Checker

F

V

E

Exercise 1 — Faces, Vertices, Edges

1. How many faces does a cube have?
2. How many vertices does a cube have?
3. How many edges does a triangular prism have?
4. How many faces does a square pyramid have?
5. How many vertices does a square pyramid have?
6. How many faces does a tetrahedron have?
7. How many edges does a cube have?
8. How many vertices does a triangular prism have?
9. How many faces does a triangular prism have?
10. How many edges does a tetrahedron have?

Exercise 2 — Euler's Formula (F + V − E = 2)

Find the missing value using F + V − E = 2

1. F=6, E=12. Find V.
2. F=5, E=9. Find V.
3. F=5, E=8. Find V.
4. F=4, E=6. Find V.
5. F=8, E=18. Find V.
6. F=6, V=8. Find E.
7. F=5, V=6. Find E.
8. F=5, V=5. Find E.
9. V=4, E=6. Find F.
10. V=8, E=12. Find F.

Exercise 3 — Nets and Faces

How many faces (shapes) are in the net of each 3D shape?

1. Cube
2. Cuboid
3. Triangular prism
4. Square pyramid
5. Tetrahedron
6. A net has 4 triangular shapes and 1 square. What 3D shape does it make? (1=triangular prism, 2=square pyramid, 3=cube, 4=tetrahedron)
7. A net has 6 square shapes. What 3D shape? (use code above)
8. How many rectangles are in the net of a triangular prism?
9. How many triangles are in the net of a triangular prism?
10. How many triangles are in the net of a tetrahedron?

Exercise 4 — Identify the Shape

Use code: 1=Triangular Prism, 2=Square Pyramid, 3=Cube, 4=Cuboid, 5=Tetrahedron

1. F=6, V=8, E=12 (all square faces) — shape code?
2. F=5, V=5, E=8 — shape code?
3. F=5, V=6, E=9 — shape code?
4. F=4, V=4, E=6 — shape code?
5. F=6, V=8, E=12 (rectangle faces) — shape code?
6. Has 2 triangular faces and 3 rectangular faces — shape code?
7. Has 1 square base and 4 triangular faces — shape code?
8. Has all equal square faces — shape code?
9. A prism with triangular cross-section — shape code?
10. All 4 faces are equilateral triangles — shape code?

Exercise 5 — Cross-Sections

Enter the code: 1=Circle, 2=Rectangle, 3=Triangle, 4=Square, 5=Hexagon

1. Slice a sphere — cross-section shape code?
2. Slice a cube horizontally — cross-section shape code?
3. Slice a cylinder horizontally — cross-section shape code?
4. Slice a cylinder vertically (lengthways) — cross-section shape code?
5. Slice a triangular prism perpendicular to its length — cross-section shape code?
6. Slice a cuboid horizontally — cross-section shape code?
7. Slice a square pyramid horizontally near the base — cross-section shape code?
8. Slice a regular hexagonal prism perpendicular to its length — cross-section shape code?
9. Slice a cone horizontally — cross-section shape code?
10. Slice a triangular prism along its length (horizontal) — cross-section shape code?

Practice — 20 Questions

1. Faces on a cube?
2. Edges on a triangular prism?
3. F=4, E=6. Find V (Euler).
4. Net of a cube has how many shapes?
5. Cross-section of sphere (code 1=circle,2=rect,3=tri,4=sq)?
6. Vertices on a square pyramid?
7. Faces on a tetrahedron?
8. F=5, V=6. Find E (Euler).
9. Net of triangular prism has how many shapes?
10. Cylinder horizontal cross-section code?
11. Edges on a cube?
12. Vertices on a triangular prism?
13. F=6, V=8. Find E (Euler).
14. Net of square pyramid has how many shapes?
15. Cube cross-section code (horizontal slice)?
16. Faces on a square pyramid?
17. Edges on a tetrahedron?
18. F=5, E=8. Find V (Euler).
19. Triangular prism cross-section perpendicular to length code?
20. Vertices on a tetrahedron?

Challenge — 8 Hard Questions

1. A polyhedron has 10 faces and 15 edges. How many vertices?
2. A prism has a pentagonal cross-section. How many faces does it have?
3. A prism has a pentagonal cross-section. How many edges does it have?
4. A pyramid has a hexagonal base. How many faces does it have?
5. A pyramid has a hexagonal base. How many edges does it have?
6. A solid has F=7, V=7, E=12. Does it satisfy Euler's formula? Enter 1 for yes, 0 for no.
7. How many faces does a hexagonal prism have?
8. A pyramid has 8 edges. How many sides does its base polygon have?