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Lesson 3 of 4 · Painted cube cut into smaller cubes

Partial painting

Cubes and Dice · for IPMAT Indore, IPMAT Rohtak and JIPMAT

The exam method

  1. Partial painting. Paint only the faces named; a cube is coloured if it lies on any of them; subtract the shared edge once for adjacent faces.

Worked examples

Example 1Sitter

A cube painted on all faces is cut into 125 equal cubes. How many have no painted face?

Example 4Typical

Opposite faces are violet, indigo and orange; 512 small cubes have no paint. How many show only violet?

Formulas you need

n=edge of big cubeedge of small cube,total=n3n = \dfrac{\text{edge of big cube}}{\text{edge of small cube}},\quad \text{total} = n^3

Picked from the Painted cube cut into smaller cubes note for this micro-concept automatically. The whole note: Painted cube cut into smaller cubes.