# Look Inside (1)

- Author:
- Renáta Vágová

- Topic:
- Geometry, Solids or 3D Shapes

## Look Inside

*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*

*try to answer the following questions:**a)*

*How many layers of cube C do you have to unwrap to get to one single unit cube?*

*b)*

*How many unit cubes does each layer have?*

*c)*

*How many unit cubes are hidden in cube C that cannot be seen at all?*

*d)*

*How many unit cubes of the visible layer touch the faces of unit cubes of the previous layer?*

*e)*

*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?*To solve the problem you can use the following GeoGebra Applet, where you can also change the colour of individual unit cubes (one click - yellow colour, two clicks - blue colour, three clicks - the original orange colour). You try to colourfully highlight the wanted unit cubes in questions a)-e).