Difference between revisions of "2006 AMC 10A Problems/Problem 24"
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== Problem == | == Problem == | ||
| − | Centers of adjacent faces of a unit cube are joined to form a regular octahedron. What is the volume of this octahedron? | + | Centers of adjacent faces of a unit [[cube (geometry) | cube]] are joined to form a regular [[octahedron]]. What is the volume of this octahedron? |
<math>\mathrm{(A) \ } \frac{1}{8}\qquad\mathrm{(B) \ } \frac{1}{6}\qquad\mathrm{(C) \ } \frac{1}{4}\qquad\mathrm{(D) \ } \frac{1}{3}\qquad\mathrm{(E) \ } \frac{1}{2}\qquad</math> | <math>\mathrm{(A) \ } \frac{1}{8}\qquad\mathrm{(B) \ } \frac{1}{6}\qquad\mathrm{(C) \ } \frac{1}{4}\qquad\mathrm{(D) \ } \frac{1}{3}\qquad\mathrm{(E) \ } \frac{1}{2}\qquad</math> | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See Also == | == See Also == | ||
*[[2006 AMC 10A Problems]] | *[[2006 AMC 10A Problems]] | ||
Revision as of 11:22, 30 October 2006
Problem
Centers of adjacent faces of a unit cube are joined to form a regular octahedron. What is the volume of this octahedron?
Solution
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