# Look Inside (1)

- Author:
- Renata Vagova

- 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?
*(Start with the visible (outer) layer and write the answer in the form "'number' and 'number' and 'number' and etc.")

*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?
*

**You can use the following GeoGebra Applet with the printed "Navigation Guide" to solve the problem. Applet Instructions: a) Use the sliders to look inside cube C (1st PRISM - 5th PRISM) b) Use 'FRONT VIEW OF A CUBE' to hide/show cubes in 1st PRISM - 3rd PRISM. c) Click on the individual cubes to change their colour (one click - yellow colour, two clicks - red colour, three clicks - green colour).**

*FEEL FREE TO BE CREATIVE IN YOUR SOLUTION :-)*