Question

A cube is painted blue on two adjacent faces. It is painted brown on the faces opposite to blue faces and yellow on the remaining faces. After being cut into sixty-four smaller cubes of equal size, what is the fraction of the cubes which have exactly one face painted blue?

Answer 1

Given : A cube is painted blue on two adjacent faces. It is painted brown on the faces opposite to blue faces and yellow on the remaining faces. then cut into sixty-four smaller cubes of equal size,

To Find :  what is the fraction of the cubes which have exactly one face painted blue?​

Solution:

Cube is cut  in 64 Cubes

4 x 4  x 4  = 64

cube is painted blue on two adjacent faces

Hence at one edge  two faces will have blue color

2 x  (16 - 4)  = 24

24 cubes  have exactly one face painted blue

Fraction = (24/64)  = 3/8

If Only one face colored blue and no other color then  

2 * (4 - 2)(4 - 2)  =  8  

8 Cubes have only  one face painted blue

Fraction = 8/64 = 1/8

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