AHSME 1980 Problem 16

Four of the eight vertices of a cube are the vertices of a regular tetrahedron. Find the ratio of the surface area of the cube to the surface area of the tetrahedron. $\text{(A)} \ \sqrt 2 \text{(B)} \ \sqrt 3 \text{(C)} \ \sqrt{\frac{3}{2}} \text{(D)} \ \frac{2}{\sqrt{3}} \text{(E)} \ 2$