In the question "Little wooden cubes each with a side of one inch are put together to form a solid cube with a side of three inches. This big cube is then painted red all over on the outside. When the big cube is broken up into the original little ones, how any cubes will have paint on two sides?" …

Question

In the question "Little wooden cubes each with a side of one inch are put together to form a solid cube with a side of three inches. This big cube is then painted red all over on the outside. When the big cube is broken up into the original little ones, how any cubes will have paint on two sides?" the solution given is "To make a cube of side of 3 inch, total 27 cubes will be needed of 1 inch And cubes having 2 side painted will be 2nd cube of 1st and 3rd row of every surface. So total will be 8 small cubes having 2 side painted." but if we consider the bigger cube into 3 layers, then in the top and bottom layer will have 4 cubes with 2 sides colored each so this makes 8 cubes and in the middle layer he cubes at corner i.e. 4 small cubes will also get colored on two sides. Then the solution must be 12 but 8 is given as solution. Please clarify me on this doubt. i need a clear explanation for this question

Rahul Tiwari · Answer

hey what i think  is ,,,,,27 cubes are required to make a 3 inch cube, made up of 1 , so each layer has 9 one inch cubes , if we paint the bigger cube i.e of 3 inch made up of 1 inch cubes ,so in the first layer ,,2nd cube of 1st row , 1st cube of 2nd row , 3rd cube of 2nd row and 2nd cube of 3rd row will get 2 sides painted,so the front and the back layer is same ,so 4+4 = 8 in two layers ,,in the middle one layer, 1st and 3rd cube of 1st row and 1st and 3rd cube of 3rd row .so the answer came is 12 .But in the book the given ans is 8   ...... Isn't it a mistake in printing ????

Shivankan Gupta · Answer

Hi Hariha,We need to make a cube with each side as 3 inch from cubes of sides of 1 inch. So, we need each side o the bigger cube to have 3 smaller cubes and not 4 as you are assuming incorrectly.

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