Spatial Reasoning and Visualization Flashcards

A rectangular box has a length of 4, width of 3, and height of 2. What is its volume?

Answer: 24

Volume of a rectangular box = length × width × height = 4 × 3 × 2 = 24.

If a shape is rotated 270° clockwise, this is the same as rotating it how many degrees counter-clockwise?

Answer: 90°

Rotating 270° clockwise is the same as rotating 90° counter-clockwise, since 360° − 270° = 90°.

How many lines of symmetry does a regular hexagon have?

Answer: 6

A regular hexagon has 6 lines of symmetry — 3 connecting opposite vertices and 3 connecting midpoints of opposite sides.

Looking at a 3×3 grid of blocks, if you remove one corner block, how many blocks remain?

Answer: 8

A 3×3 grid contains 9 blocks; removing 1 corner block leaves 8 blocks.

If two parallel lines are cut by a transversal, which pair of angles are equal?

Answer: Alternate interior angles

Alternate interior angles (Z-angles) are equal when two parallel lines are cut by a transversal.

A water tank is a cylinder with a radius of 2 m and a height of 5 m. Using π ≈ 3.14, what is the approximate volume?

Answer: 62.8 m³

Volume = π × r² × h = 3.14 × 4 × 5 = 3.14 × 20 = 62.8 m³.