Find the relationship describing the volume (V) of a cube as a function of the length of the diagonal going through the cube (d). and evaluate it for a diagonal length of d = 1.2.
Find the relationship describing the volume (V) of a cube as a function of the length of the diagonal going through the cube (d). and evaluate it for a diagonal length of d = 1.2.
After applying Pythagoras' theorem twice, we get... "internal diagonal"=
where "x" is the length of a side of the cube.
The volume of the cube is
Since
then
which is the cube volume.
This allows us to express the cube volume as a function of the internal diagonal length.
The internal diagonal goes from the bottom right-corner of the base of the cube to the
top-left corner of the facing side,
or from the bottom left-corner to the facing side's top right-corner.
I'll be the first to admit that my sketch is not drawn well!
The sides should appear to be the same lengths.