MathDB
Surface Area Ratios

Source:

December 31, 2005
geometryratio3D geometrytetrahedroncongruent triangles

Problem Statement

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. (A) 2(B) 3(C) 32(D) 23(E) 2\text{(A)} \ \sqrt 2 \qquad \text{(B)} \ \sqrt 3 \qquad \text{(C)} \ \sqrt{\frac{3}{2}} \qquad \text{(D)} \ \frac{2}{\sqrt{3}} \qquad \text{(E)} \ 2
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