Math Adventures/Tetrahedron in a Cube

Tetrahedron in cube

A tetrahedron can be inscribed within a cube such that four of the eight vertices of the cube are coincident with the four vertices of the tetrahedron, as shown in the diagram on the right.

1. Calculate the ratio of the area of the cube to the area of the tetrahedron.
2. Calculate the ratio of the volume of the cube to the volume of the tetrahedron.