Question

A cube is painted red on all of its faces and then cut into 216 small cubes of equal size Now answer the following question
The total number of small cubes which are painted red exactly on three surfaces is​

Answer 1

Given :  A cube is painted red on all of its faces and then cut into 216 small cubes of equal size

To Find : The total number of small cubes which are painted red exactly on three surfaces ​

Solution:

At each vertex cube has 3 three surfaces painted red

A cube has 8 vertex

Hence 8 cubes are painted red exactly on three surfaces

216 = 6 x 6 x 6

Exactly 3 faces painted  =  8

Exactly 2 faces painted  = 12 * (6 - 2)  = 48

Exactly 1 face  painted  = 6 * (6 - 2)(6-2)  = 96

No Face painted = (6 - 2)³  = 64

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