[i][i]Imagine an unlimited number of small unit cubes (all the same size 1×1×1). From these unit cubes, you start to build bigger and bigger cubes in such a way that a cube will be wrapped into other unit cubes.[br]This “unit cube wrap” can be called a layer. Then imagine the built cube C of the size of 6×6×6 unit cubes. Using the GeoGebra applet, try to answer the following questions: [/i][br][br][b][i]a)    [/i][/b][i]How many layers of cube C do you have to unwrap to get to the smallest possible cube built from small unit cubes?[/i][br][br][b][i]b)    [/i][/b][i]How many unit cubes does each layer have? [/i][br][br][b][i]c)     [/i][/b][i]How many unit cubes are hidden in cube C[sub] [/sub]that cannot be seen at all? [/i][br][br][b][i]d)    [/i][/b][i]How many unit cubes of the visible layer touch the faces of unit cubes of the previous[br]layer? [/i][br][br][b][i]e)     [/i][/b][i]Remove the unit cubes from cube C that have just three touching faces with the other unit[br]cubes. How many unit cubes remain in the visible layer? [/i] [/i]