11+ Spatial Awareness 5 — Questions and Answers
Question 1: A 3×3×3 cube is made of 27 unit cubes. If the entire outer surface is painted, how many unit cubes have NO paint on them?
- 0
- 1 (Correct answer)
- 6
- 8
Correct answer: 1
Only the centre cube (completely surrounded by other cubes on all 6 sides) has no painted faces. There is exactly 1 such cube in a 3×3×3 arrangement.
Question 2: If you cut a Möbius strip in half along its centre line, what do you get?
- Two separate Möbius strips
- One longer strip with two twists (Correct answer)
- Two linked rings
- A flat rectangle
Correct answer: One longer strip with two twists
Cutting a Möbius strip along its centre line produces one longer strip with two half-twists (a full twist), not two separate strips.
Question 3: A shadow is cast by a sphere using a point light source. What shape is the shadow?
- Square
- Circle (Correct answer)
- Oval
- Irregular
Correct answer: Circle
A sphere casts a circular shadow because its cross-section from any direction is a circle.
Question 4: Looking at an isometric drawing (3D view) of steps, you count 3 steps going up from left to right. How many unit cubes make up this shape if each step is 1 cube deep?
- 3
- 6 (Correct answer)
- 9
- 12
Correct answer: 6
Step 1 (bottom): 3 cubes wide × 1 deep = 3. Step 2: 2 cubes. Step 3: 1 cube. Total = 3 + 2 + 1 = 6 cubes.
Question 5: A piece of paper is folded in half, then in half again. A corner is cut off. How many holes appear when the paper is unfolded?
- 1
- 2
- 4 (Correct answer)
- 8
Correct answer: 4
Folding in half twice creates 4 layers. Cutting a corner goes through all 4 layers, creating 4 holes when unfolded.
Question 6: A hexagonal prism has how many edges?
- 12
- 15
- 18 (Correct answer)
- 24
Correct answer: 18
A hexagonal prism has 18 edges: 6 on the top hexagon, 6 on the bottom hexagon, and 6 vertical edges connecting them.
11+ Spatial Awareness 5
A 3×3×3 cube is made of 27 unit cubes.
If the entire outer surface is painted, how many unit cubes have NO paint on them?