The distance between centres of two adjacent faces of a cube is
$8$cm. What is the side length of the cube?
I can make an equilateral triangle by cutting off the corner of a
cube. If the area of the largest equilateral triangle I can
create in this way is $140$cm$^2$, what is the side length of
this cube?
A third cube has an edge length of $12$cm. At each vertex, a
tetrahedron with three mutually perpendicular edges of length
$4$cm is cut away. Can you find the volume and the surface area
of the remaining solid?
