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

Orange and Blue

Answer

Red and Yellow

Answer

Green and Blue

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

The original 3D shape had a hollow interior

Answer

The net represents a torus (donut shape)

Answer

The unfolding procedure was valid but unusual

Question 3

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

Accepted Answer

12

Answer

10

Answer

11

Answer

14

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

A net and asks you to solve a related math equation

Answer

Two nets and asks you to combine them into one shape

Answer

A series of 2D shapes and asks you to find the odd one out

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

All 6 squares are in a single straight row

Answer

The shape is symmetric about at least one axis

Answer

The shape contains no more than 2 squares in any single row

Question 6

Two cube nets are exact mirror images of each other. When both are folded into blank (unmarked) cubes, the result is:

Accepted Answer

Two identical, indistinguishable cubes

Answer

Two cubes that cannot be superimposed on each other

Answer

One valid cube and one collapsed shape

Answer

Two cubes with opposite face orientations that look different

Question 7

Mentally rotating a 3D object to match it with its correct flat net — as required in CFAT spatial tests — is an example of:

Accepted Answer

Spatial reasoning

Answer

Crystallographic analysis

Answer

Mathematical induction

Answer

Sequential pattern recognition