Spatial Visualization Tasks Flashcards

A square piece of cardboard is cut diagonally in half to make two triangles. The two triangles are rearranged to form a rectangle (not a square). What are the proportions of the rectangle?

Answer: 1:2

Two right isosceles triangles from a square reassemble into a rectangle with length twice the width (ratio 2:1), or equivalently 1:2.

Looking at a transparent box from above, you see a 4×3 rectangle. Looking from the front, you see a 4×2 rectangle. What are the dimensions of the box?

Answer: 4×3×2

Top view (4×3) gives length and width; front view (4×2) gives length and height, so the box is 4 long, 3 wide, and 2 tall.

A sphere is cut by a single flat plane. What shape is the cross-section always?

Answer: A circle

Any flat plane cutting through a sphere always produces a circular cross-section, regardless of angle.

You travel 3 miles north, then 4 miles east. How far are you in a straight line from your starting point?

Answer: 5 miles

Using the Pythagorean theorem: √(3² + 4²) = √(9 + 16) = √25 = 5 miles.

A square is rotated 45° and placed inside a larger square so that its corners touch the midpoints of the larger square's sides. What fraction of the larger square does the rotated square cover?

Answer: 1/2

A square rotated 45° with corners at the midpoints of a larger square covers exactly half the larger square's area.

A soldier faces East. He turns left 90°, then turns right 180°, then turns left 90°. What direction is he now facing?

Answer: East

Starting East: left 90° = North; right 180° = South; left 90° = East — back to the original direction.

How many distinct ways can a standard 2×2 Rubik's cube face be oriented if you can only rotate the entire cube (not individual pieces)?

Answer: 24

A cube has 24 possible orientations (6 faces can be on top × 4 rotations per face).