MathDB
1997 AJHSME #17 - Cube Diagonals

Source:

June 30, 2011
geometry3D geometryAMC

Problem Statement

A cube has eight vertices (corners) and twelve edges. A segment, such as xx, which joins two vertices not joined by an edge is called a diagonal. Segment yy is also a diagonal. How many diagonals does a cube have?
[asy]draw((0,3)--(0,0)--(3,0)--(5.5,1)--(5.5,4)--(3,3)--(0,3)--(2.5,4)--(5.5,4)); draw((3,0)--(3,3)); draw((0,0)--(2.5,1)--(5.5,1)--(0,3)--(5.5,4),dashed); draw((2.5,4)--(2.5,1),dashed); label("xx",(2.75,3.5),NNE); label("yy",(4.125,1.5),NNE); [/asy]
<spanclass=latexbold>(A)</span> 6<spanclass=latexbold>(B)</span> 8<spanclass=latexbold>(C)</span> 12<spanclass=latexbold>(D)</span> 14<spanclass=latexbold>(E)</span> 16<span class='latex-bold'>(A)</span>\ 6 \qquad <span class='latex-bold'>(B)</span>\ 8 \qquad <span class='latex-bold'>(C)</span>\ 12 \qquad <span class='latex-bold'>(D)</span>\ 14 \qquad <span class='latex-bold'>(E)</span>\ 16