11+ Spatial Awareness 5

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?

Accepted Answer

1

Answer

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?

Accepted Answer

One longer strip with two twists

Answer

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?

Accepted Answer

Circle

Answer

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?

Accepted Answer

6

Answer

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?

Accepted Answer

4

Answer

Folding in half twice creates 4 layers. Cutting a corner goes through all 4 layers, creating 4 holes when unfolded.

11+ Practice Test

11+ Practice Test

11+ Spatial Awareness 5