Perplexing math question?

Question

A cube is made of chocolate, but the outside is covered with red
icing.
If the cube is cut into 125 smaller cubes of exactly the
same size, how many of the cubes will have at least 2 of their
sides with icing?

Answer 1

44

the cubed root of 125 is 5... this means the cube was 5x5x5. 8 of these are the coners (having 3 sides red) then that leaves 12 edges with 3 cubes no coners (2 sides red).

8 + 12*3 = 44

Answer 2

The only place where at least two sides have icing would be where the cube's faces meet. Since you have 125 smaller cubes, 5 cubes make up an edge. Since there are 12 edges, 5 X 12 results in 60 cubes, but since you counted each corner 3 times you have to take off 2 for each corner. There are 8 corners, and so you take off 16 from the 60. You get 44 cubes.

Answer 3

44

To obtain 125 cubes you have to divide your large cube in 25 squares per side in a 2D drawing.
It is like a 'magic cube' but instead of 9 different colors per side you have 25. How do you know it is 25? First you have to know that the volume of the cube is side*3. So you can think 125 as 5 x 5 x 5 -you are not given the lenght of the side but the number of smaller cubes. This way you know each side will have 25 (5x5) small cubes and the third, the one that makes it 3D is the other 5 that makes it 125.
So, now you know you have 25 small cubes per side and it is better to draw it. That way you will see that the ones on the edges are those that have 2 sides with icing. Do not double count and you will see 44.
GOOD LUCK!!

Answer 4

The correct answer is 44. Another way of showing this is to consider all the cubes that DON'T meet the requirements. To begin with there is a 3x3x3 cube in the middle of the 5x5x5 cube where none of the faces will have icing.

So that's 27 cubes that don't fit the bill.

If we now look at any one of the faces it will be clear that the 3x3 cubes in the middle of the face only have one face that is covered with icing. So that's 3x3 = 9 and since there are 6 faces that makes 9x6 = 54.

So that's another 54 cubes not meeting the requirements.

In all that makes 27 + 54 = 81

125 (5x5x5) minus 81 equals 44.

Answer 5

The cubes on the periphery will be covered with red icing. There are 6 sides in a cube and in each side the number of cubes with two sides of red icing will be 10 each. That will make 60 cubes. However the cubes on the vertical edges just below the 60 cubes will also be covered with two sides of icing. On each edge there will be 3 cubes and there are 4 vertical edges and therefore the number of cubes on the edges will be 12. Hence the total number of cubes with at least 2 edges of red icing will be 72.

Answer 6

At least two, that means only the ones on its edges.
The cube's dimensions are 5 by 5 by 5
So if you envision the cube you would know that there are 12 sides.
SO the answer would be 4 times 5 + 8 (other sides) times 3 (they share two cubes with the previous ones) = 44.

Answer 7

If it was cut into 125 smaller cubes, then it was cut 5x5x5. Only the pieces on the edges or in the corners would have icing on two sides or more.

There are 8 corners, and 12 edges where 3 pieces would not be corners. So 8 + 12*3 = 44.

Answer 8

That means your cube is 5x5x5 and have a face of 5x5. To have at least two sides with icing you are talking about the sides fo the faces. Do not double count, on the top face you have 3x4+4 corners, i.e. 16 of said cubes. Same on the bottom face, plus 3x4 on the sides, so there are 44 said cubes.

Answer 9

I am wondering ... how can cut a cube in 125 smaller cubes of exactly the same size? Is that even possible???

Answer 10

Impossible as you cannot cut a cube into 125 cubes as that would mean cutting each square side into 5 squares