Spatial Reasoning Flashcards

Three cubes are stacked vertically. How many flat faces are hidden (touching another cube or the ground) in total?

Answer: 5

Each junction between two cubes hides 2 faces (one from each cube), giving 2 junctions × 2 = 4 hidden faces, plus 1 face on the ground = 5 total.

A square is rotated 45° and placed inside a larger square so its corners touch the midpoints of the outer square's sides. What shape is formed between the two squares?

Answer: 4 right triangles

The rotated inner square cuts each corner of the outer square into a right isosceles triangle, creating 4 right triangles in the corners.

You are facing North. You turn 90° to your right, then 180°, then 90° to your left. Which direction are you now facing?

Answer: South

Starting North: +90° right → East; +180° → West; +90° left → South.

A hollow cylinder is cut in half lengthwise. What is the shape of the flat cut surface?

Answer: Rectangle

Cutting a cylinder lengthwise along its axis reveals a flat rectangular cross-section whose width equals the diameter and length equals the cylinder's height.

Four identical L-shaped pieces are arranged to form a 4×4 square. Each L-shape covers exactly 4 unit squares in an L configuration. How many unit squares does the entire 4×4 square contain?

Answer: 16

A 4×4 grid contains 4 × 4 = 16 unit squares, and four L-shaped tetrominoes each covering 4 squares account for all 16.

An object is viewed from the front and appears as a triangle. Viewed from above, it appears as a square. Which shape could this object be?

Answer: Square pyramid

A square pyramid has a square base (seen from above) and triangular faces visible from the front elevation.

A 2×4 rectangle is divided into exactly 8 unit squares arranged in 2 rows of 4. How many different rectangles of any size can be traced within this grid, including the whole shape?

Answer: 15

In a 2×4 grid, the number of rectangles is C(3,2) × C(5,2) = 3 × 10 = 15, using the formula for counting rectangles in an m×n grid.