Difference between revisions of "2015 AMC 10B Problems/Problem 17"
| Line 14: | Line 14: | ||
label("5",(5,4,0)--(0,4,0),SE); | label("5",(5,4,0)--(0,4,0),SE); | ||
</asy> | </asy> | ||
| − | + | <math>$\textbf{(A) } \dfrac{75}{12} | |
| − | $\textbf{(A) } \dfrac{75}{12} | ||
\qquad\textbf{(B) } 10 | \qquad\textbf{(B) } 10 | ||
\qquad\textbf{(C) } 12 | \qquad\textbf{(C) } 12 | ||
\qquad\textbf{(D) } 10\sqrt2 | \qquad\textbf{(D) } 10\sqrt2 | ||
\qquad\textbf{(E) } 15 | \qquad\textbf{(E) } 15 | ||
| − | + | </math> | |
Revision as of 13:47, 6 March 2015
Problem
The centers of the faces of the right rectangular prism shown below are joined to create an octahedron, What is the volume of the octahedron?
![[asy] import three; size(2inch); currentprojection=orthographic(4,2,2); draw((0,0,0)--(0,0,3),dashed); draw((0,0,0)--(0,4,0),dashed); draw((0,0,0)--(5,0,0),dashed); draw((5,4,3)--(5,0,3)--(5,0,0)--(5,4,0)--(0,4,0)--(0,4,3)--(0,0,3)--(5,0,3)); draw((0,4,3)--(5,4,3)--(5,4,0)); label("3",(5,0,3)--(5,0,0),W); label("4",(5,0,0)--(5,4,0),S); label("5",(5,4,0)--(0,4,0),SE); [/asy]](http://latex.artofproblemsolving.com/0/f/e/0fecfb360827e29c3e9ad69126c0215a16cfd2ab.png)
