CFAT Spatial Ability: 2D Unfolding 5

Question 1

A cube has a different color on each face. Green is opposite Red, and Blue is opposite Yellow. Which must be the third pair of opposite faces?

Accepted Answer

Orange and Purple

Answer

With Green-Red and Blue-Yellow identified, the only remaining pair of faces must be Orange and Purple.

Question 2

When unfolding a convex polyhedron, if the resulting flat shape has an interior square hole (empty space completely surrounded by other squares), this means:

Accepted Answer

The net is invalid — valid nets for convex shapes have no interior holes

Answer

A valid net for a convex polyhedron is a simply-connected flat region with no holes — any interior gap makes it invalid.

Question 3

A dodecahedron has 12 pentagonal faces. Its flat net contains how many pentagons?

Accepted Answer

12

Answer

A net must include every face of the 3D shape, so a dodecahedron's net contains all 12 pentagons.

Question 4

On the CFAT, a typical 2D unfolding question presents:

Accepted Answer

A 3D shape and asks you to choose the correct net from four options

Answer

CFAT unfolding questions typically show a 3D object and require selecting which of four answer choices is the correct flat net.

Question 5

Which condition is necessary — but not by itself sufficient — for a hexomino (6-square shape) to be a valid cube net?

Accepted Answer

All 6 squares are connected with no isolated pieces

Answer

Connectivity is necessary for any net, but not all connected 6-square shapes fold correctly — for example, a 2×3 grid is connected but invalid.

(CFAT) Canadian Forces Aptitude Test Practice Test

(CFAT) Canadian Forces Aptitude Test Practice Test

CFAT Spatial Ability: 2D Unfolding 5