Question

»
A cube is painted green on
all its
surfaces. If it is cut
125 smaller
cubes
of the same size,
then how many
cubes will
have
two side
painteet
in green?​

Answer 1

A cube painted blue on all faces, is divided into125 small cubes. l x bx h = 125

ie, its length= 5

Breadth = 5

Height = 5

A cube has 6 faces

Let A & B be 1st pair of opposite lateral faces

C & D be 2nd pair of opposite lateral faces

E be Top face

F be bottom face

Now we find out the total number of painted faces =

Face A contains = 25 cubes ( l x h = 5x5)

Face B contains= 25 cubes( l x h = 5x5)

Face C contains = 15 cubes( b x h = 3 x5) we take breadth as 3, as corner cubes have already been counted with face A & B.

Face D contains =15 cubes( b xh= 3x5)

Face E contains= 9 cubes ( l x b= 3x3)

Face F contains = 9 cubes ( l x b= 3x3)

So total number of painted faces = 25+25+15+15+9+9= 98 cubes

Therefore, the number of cubes not painted on any of the faces, which lie inside = 125 — 98 = 27