All the faces of a cube are painted with blue colour. then it is cut into 125 small equal cubes. how many small cubes will be formed having no face coloured ?
Answers
Now, consider the large cube. It is broken into 125 equal pieces. The cubes which are in edges, corners, centres are painted.
Imagine a cube like a bread loaf. To cut it to 125 pieces, you should make 4 cuts (Which makes 5 pieces) vertically, then horizontally in a single side like this:
Then you should place the cube such that the cut edge is top perpendicular and make 4 cuts horizontally. This gives you 125 pieces.
Now you can imagine that the inner cube with uncoloured cubes has an outer layer of cubes, rather an envelope of coloured cubes.
The outer layer will be the 5x5x5 cube and the inner cube (UNCOLOURED) will be 3x3x3.
So, in total, 27 cubes without any coloured edges.
To explain mathematically,
Coloured edges,
top layer full cubes = 25 cubes
bottom layer full cubes = 25 cubes
uncounted edge cubes (4x3) = 12 cubes
uncounted centre cubes (4x9) = 36 cubes
---------------------------------------
total coloured cubes = 98 cubes
total uncoloured cubes = total cubes - total uncoloured
= 125-98
= 27
Answer is 27
Answer: There will be 27 cubes formed which will have no side coloured.
Step-by-step explanation: