Find the number of cubes ? Explain Clearly?

Question

There is a cube which is painted on all sides with Red colour, which is then divided into 125 cubes of equal size.Find the number of cubes which are having color at the 3 faces ,number of cubes having color at 2 faces and colour only at one face, and also cubes having no color .

Answer 1

Visualize this....

When the cube painted red is divided into 125 cubes, you would have to figure out how are the cubes tiled up to get to the answer.

Volume is Length X Breadth X Height, and since it's cubical, it should be cube root of 125, which is 5. Which means each side of the structure has got 5 rows of cubes. Each row is also 5 cubes.

You need some visualization here, i suggest you draw out and slowly cross out.

(a) For the sides painted with 3 red faces, it should be the ones taking up the corner, which is 8.

(b) For those painted with 2 red faces, it should be all at the sides, minus the corners which has been accounted tor in (a). 12 X 3 = 36.

c s s s c
_ _ _ _ _

(c) One each side of the structure, there are 3 X 3 painted with oly one face, So there are 9 cubes per side makes it 9X6 = 54 cubes.

(d) And the rest without any color? simply take 125 - (54 + 36 +8) = 27 or if you can visualize the internal structure, taking out the first layer it's 3 X 3 X 3 = 27.

Hope this helps...

Answer 2

OK. So a big cube is cut up into 125 small cubes.

Say the big cube was 5 feet on a side and the small cubes are 1 foot on a side.

How many cubes will have color on 3 faces? Exactly the 8 cubes that came out of the 8 corners of the larger cube.

Now **you** use a bit of logic and counting on your fingers to figure out the other 3 answers ☺


Doug

Answer 3

First of all, since it is divided into 125 cubes of equal size, each edge is divided into (125)^1/2=5 parts, and each side is divided into 5^2=25 parts.

Now we count the number of vertae of the original cube: 8, and that is the number of smaller cubes with 3 coloured faces.

Then we count the number of smaller cubes on each edge of the original cube, excluding those at the vertae: 12*(5-2=3)=36. That is the number of smaller cubes with 2 couloured faces.

Then we count the number of smaller cubes on each side of the original cube, excluding those already accounted for: 6*(25-4-4*3=9)=54. That is the number of smaller cubes with 1 couloured face.

Finally, we subtract the sum of the number of smaller cubes mentioned above, i.e. coloured small cubes, from the total number of 125: 125-8-36-54=27. That is the number of uncoloured small cubes.

Answer 4

number of cubes have color on

3 faces: 8 (corners of cube)
2 faces: 36 (3 times 12 edges of cube)
1 face: 54 (center of each face 3x3 times 6 faces of cube)
no color: 27 (3x3x3 inside the cube)

Answer 5

huh? im not a maths genius so dont go with my answer.. 99?

Answer 6

http://magegame.ru/?rf=6972756e6b615f37

Answer 7

what ...i guess simple folk wouldnt understand