CFAT Spatial Ability: 3D Folding 5

Question 1

A 3×3×3 cube is painted red on all 6 surfaces, then cut into 27 small unit cubes. How many small cubes have exactly 2 red faces?

Accepted Answer

12

Answer

The 12 edge pieces of a 3×3×3 cube (not at corners) each sit on exactly 2 painted surfaces, giving them exactly 2 red faces.

Question 2

A 3×3×3 cube painted red on all faces is cut into 27 small cubes. How many small cubes have exactly 3 red faces?

Accepted Answer

8

Answer

The 8 corner pieces each sit where 3 faces of the large cube meet, giving them exactly 3 red painted faces.

Question 3

A right triangular prism has triangular bases and rectangular sides. How many total edges does it have?

Accepted Answer

9

Answer

A triangular prism has 9 edges: 3 edges on each triangular base (6 total) plus 3 lateral edges connecting the two bases.

Question 4

A pentagonal prism (with pentagon-shaped bases) has how many faces in total?

Accepted Answer

7

Answer

A pentagonal prism has 7 faces: 2 pentagonal end faces plus 5 rectangular side faces (one per pentagon edge).

Question 5

You want face X to be directly opposite face Y in a folded cube. In the net, faces X and Y must be:

Accepted Answer

At least 2 squares apart along any path in the net

Answer

Faces that are adjacent in the net share an edge in the cube and can never be opposite — so opposite faces must always be at least 2 squares apart in the net.

(CFAT) Canadian Forces Aptitude Test Practice Test

(CFAT) Canadian Forces Aptitude Test Practice Test

CFAT Spatial Ability: 3D Folding 5