Question

20) A solid wooden cube is painted blue on all its faces . ther is then cut
into smaller cubes with edge 1/4 th of the original cube.
Po a) How many of the smaller cubes will have only one face painted?
b) How many of the smaller cubes will have all the sides unpainted?​

Answer 1

24 Smaller cubes with one face painted , 8 Smaller cubes will have all the sides unpainted

Step-by-step explanation:

A solid wooden cube is painted blue on all its faces . ther is then cut

into smaller cubes with edge 1/4 th of the original cube.

=> number of cubes = 4* 4 * 4  = 64  cubes

3 face Painted ( all corners) =  8   Cubes

2 Face Painted  (on edge except corner)  = (4 - 2) * 12 = 24 Cubes

1 Face Painted =  6 * (4 - 2)(4 - 2)  =  24 Cubes

0 Face Painted ( all side unpainted) = (4 - 2)(4 - 2)(4 - 2)  = 8  Cubes

24 Smaller cubes with one face painted

8 Smaller cubes will have all the sides unpainted

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