Spatial Ability: 3D Folding Flashcards

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?

Answer: 12

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.

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?

Answer: 8

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

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

Answer: 9

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

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

Answer: 7

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

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

Answer: At least 2 squares apart along any path in the net

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.

A cube rests on face A (bottom). You tilt the cube 90° toward you, rotating it forward around its front bottom edge. Which face is now on top?

Answer: The original front face

Tilting the cube forward 90° rotates: front→top, top→back, back→bottom, bottom→front — so the original front face rises to the top.

A polyhedron has 5 faces, 8 edges, and 5 vertices. Applying Euler's formula (F + V − E = 2), this shape is:

Answer: Valid: 5 + 5 − 8 = 2, confirming it is a real polyhedron (square pyramid)

5 + 5 − 8 = 2, satisfying Euler's formula — this describes a valid square pyramid with 1 square base, 4 triangular faces, 5 vertices, and 8 edges.