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

Question

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

ronny123 · Answer

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

chetan2u · Answer

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

youcouldsailaway · Answer

This question should be solved in two parts. First we need to find the number of cubes that can be cut out of the larger cube and then we need to find how many of these cubes thus cut out, form the middle part of the edge.

Moreover, let's note that the cube is painted OUTSIDE on all sides. Thus,

...the top and the adjoining sides are also painted pink, i.e, all 3 sides of the edge have been painted. We will call them the "corner blocks". 
...there are blocks (ones that are not a part of any edge) that are only painted on one side. We will call them "interior blocks". 
...there are blocks that are painted on only two sides (middle block of the edge). We will call them "middle-of-the-edge blocks".

For this question, we are only concerned with middle-of-the-edge blocks.

I) Since the larger cube has sides of length 6 and the smaller cube has side of length 2, the number of cubes that can be cut on each side is 6 / 2 = 3. This includes the edges being cut into cubes.

II) A cube (of any length) has has 6 faces, 12 edges and 8 vertices.

Using this, we know that we have 3 blocks from the edge and since there are 12 edges, there are 24 corner blocks and there are 12 middle-of-the-edge blocks.

Thus answer is C.

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

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