Question

A cube , painted on all its face , is cut into 125 identical smaller cubes. (1) How many smaller cubes have no face painted options are (1) 100 (2) 81 (3) 64 (4) 27.

Answer 1

n³ = 125 = 5³
n= 5 hence, each face have 5 row and column then , form 125 cubes

now, for no of cubes without painted = ( n -2)³ = (5-2)³ = 27

27 cubes which faces have not painted
so, option (4) is correct

Answer 2

as it's a cube .. let each side be 'n ' .. so.. n³ = 125

from that we get n = 5

for finding number of cubes which have no face painted ..
we must use the formula (n -2 )³

as n = 5

by substituting we get

(5-2 )³ = 3³

we get 3³ = 27

so 27 cubes have no sides painted..

hope it helps
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