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A solid cube of side 6 is first painted pink and then cut into smaller

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A solid cube of side 6 is first painted pink and then cut into smaller  [#permalink]

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New post 16 May 2016, 02:41
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A
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  45% (medium)

Question Stats:

67% (01:36) correct 33% (01:34) wrong based on 94 sessions

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Re: A solid cube of side 6 is first painted pink and then cut into smaller  [#permalink]

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New post 16 May 2016, 03:33
A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2.

This means , we get a 3 x 3 x 3 cube
To get the the sides with just 2 faces painted, picture the edges of the each of the sides of the cube.
Apart from the corners(which have 3 faces painted), all other small cubes have 2 faces painted.

In total, we have 12 cubes of side 2 with exactly 2 sides painted

C. 12
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A solid cube of side 6 is first painted pink and then cut into smaller  [#permalink]

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New post 16 May 2016, 04:00
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Bunuel wrote:
A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?

A. 30
B. 24
C. 12
D. 8
E. 6


Hi,

the point that will be helpful always -


1) the corner cube of any BIGGER cube will have 3 faces open to air ..
2) All cubes in edges except the corner will have 2 faces outwards..
3)rest all that are vis outside will have 1 face outwards...

lets solve the Q now-


Bigger cube side is 6..
smaller cube side is 2..
so EACH edge is cut into 6/2 = 3 pieces..

Now lets apply here-


1) corner ubes - 8 - will have 3 face painted..
2) cubes in each edge = 3, out of which 2 are corner ones....
so ONE cube in each edge has two faces painted..
number of edges = 12, so number of cubes = 12*1 =12
3) Cubes with single edge painted = Total - (1) -(2)

But we are looking for 2 faces ..
ans 12
C
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Re: A solid cube of side 6 is first painted pink and then cut into smaller  [#permalink]

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New post 07 Oct 2018, 19:29
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Re: A solid cube of side 6 is first painted pink and then cut into smaller   [#permalink] 07 Oct 2018, 19:29
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