Unit 5 · Geometry

4×4×4 Painted Cube — Interior Core = ?

Lesson 4 of 6

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About this lesson

Now for a classic 3D reasoning question: a large cube built from unit cubes with all outside faces painted. When it is pulled apart, how many small cubes escaped the paint entirely? This is one of those questions that looks daunting until you know the one-line trick — after which it takes under 20 seconds.

Chapters

0:00Introduction

0:24The Question

1:00Visualising the Outer Painted Layer

1:29Isolating the Unpainted Inner Core

1:56Calculating the Total Inner Cubes & Final Selection

2:24Strategic exam tip

3:03Correct answer

Question

A 4 \times 4 \times 4 cube is built from 64 small unit cubes. All outside faces are painted. The cube is broken apart into individual unit cubes. How many unit cubes have no faces painted at all?

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