CFAT Spatial Ability: 3D Folding 3 — Questions and Answers
Question 1: A square pyramid has one square base and four triangular sides. How many total faces does this shape have?
- 4
- 5 (Correct answer)
- 6
- 8
Correct answer: 5
A square pyramid has 5 faces: 1 square base plus 4 triangular lateral faces.
Question 2: The net of a triangular prism contains exactly how many faces?
- 3
- 4
- 5 (Correct answer)
- 6
Correct answer: 5
A triangular prism has 5 faces: 2 triangular end caps and 3 rectangular side panels.
Question 3: A net consists of a central equilateral triangle with one equilateral triangle attached to each of its three edges. When folded, this creates:
- A square pyramid
- A triangular prism
- A tetrahedron (Correct answer)
- An octahedron
Correct answer: A tetrahedron
One central triangle plus three attached triangles gives 4 total faces, which fold into a tetrahedron (triangular pyramid).
Question 4: A hexagonal prism net contains two hexagonal end faces and how many rectangular side faces?
- 4
- 5
- 6 (Correct answer)
- 8
Correct answer: 6
A hexagonal prism has 6 rectangular side faces — one for each edge of the hexagonal base — plus 2 hexagonal end faces.
Question 5: A regular octahedron has 8 equilateral triangular faces. Its net therefore contains:
- 6 triangles
- 7 triangles
- 8 triangles (Correct answer)
- 10 triangles
Correct answer: 8 triangles
The net of any polyhedron contains all of its faces laid flat, so an octahedron's net has all 8 triangular faces.
Question 6: A pentagonal pyramid has a pentagon as its base and five triangular lateral faces. How many edges does this shape have in total?
- 8
- 9
- 10 (Correct answer)
- 12
Correct answer: 10
A pentagonal pyramid has 10 edges: 5 edges around the pentagon base plus 5 lateral edges rising from each base corner to the apex.
Question 7: The net of a cylinder consists of two circles and one rectangle. The dimension of the rectangle that wraps around the cylinder must equal:
- The diameter of the circular ends
- The radius of the circular ends
- The circumference of the circular ends (Correct answer)
- The area of one circular end
Correct answer: The circumference of the circular ends
The rectangle wraps around the curved surface of the cylinder, so its wrapping dimension must equal the circumference (2πr) of the circular ends.
CFAT Spatial Ability: 3D Folding 3
A square pyramid has one square base and four triangular sides.
How many total faces does this shape have?