Problem:
Four of the eight vertices of a cube are vertices of a regular tetrahedron. Find the ratio of the surface area of the cube to the surface area of the tetrahedron.
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The edges of the tetrahedron are face diagonals of the cube. Therefore, if is the length of an edge of the cube, the area of each face of the tetrahedron is
and the desired ratio is