Look Inside (1)
Look Inside
[i]Imagine you have 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. This “unit cube wrap” can be called a layer. Then you build cube C of the size of 5×5×5 unit cubes and [i][i]try to answer the following questions: [/i][/i][/i]
[i]a) [/i][i]How many layers of cube C do you have to unwrap to get to one single unit cube? [/i]
[i]b) How many unit cubes does each layer have? [br][/i](Start with the visible (outer) layer and write the answer in the form "'number' and 'number' and 'number' and etc.")
[i]c) [/i][i]How many unit cubes are hidden in cube C that cannot be seen at all? [/i]
[i]d) [/i][i]How many unit cubes of the visible layer touch the faces of unit cubes of the previous layer? [/i]
[i]e) [/i][i]Remove the unit cubes from cube C that have just three touching faces with the other unit cubes. How many unit cubes remain in the visible layer? [br][/i]
[b]You can use the following GeoGebra Applet with the printed "Navigation Guide" to solve the problem.[br][br]Applet Instructions:[br]a) Use the sliders to look inside cube C (1st PRISM - 5th PRISM)[br]b) Use 'FRONT VIEW OF A CUBE' to hide/show cubes in 1st PRISM - 3rd PRISM.[br]c) Click on the individual cubes to change their colour (one click - yellow colour, two clicks - red colour, three clicks - green colour).[br][br][i]FEEL FREE TO BE CREATIVE IN YOUR SOLUTION :-)[/i][/b]
Navigation Guide
