Mathematics course : 6th grade  How to split a cube into 3
identical pyramids  Vers le même cours en français  facebook  
twitter   mail      We shall build with cardboard and glue a
pyramid fitting into a cube.  The base of the pyramid will be
the bottom side of the cube, and the top of the pyramid will be
one of the top corners of the cube.  We shall see that the
volume of this pyramid is exactly 1/3 of the volume of the cube.
Moreover, we shall reconstruct the cube with three identical
pyramids like this one.  To build the pyramid, we begin with a
model (see video for details).  Click on image to enlarge   We
cut the sheet according to the model.   And we fold and paste to
get a pyramid.   We build 3 pyramids on the same model. And we
can see that they fit exactly into a cube.    Do the three
pyramids fill in the cube entirely ? Or could there be a void
inside ? Reasoning on the angles of the various planes, on sees
that there can be no void inside. The cube is fully filled.
Therefore the volume of the in