Difference between revisions of "2015 AMC 10B Problems/Problem 17"
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+ | ==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> | ||
+ | |||
+ | $\textbf{(A) } \dfrac{75}{12} | ||
+ | \qquad\textbf{(B) } 10 | ||
+ | \qquad\textbf{(C) } 12 | ||
+ | \qquad\textbf{(D) } 10\sqrt2 | ||
+ | \qquad\textbf{(E) } 15 | ||
+ | $ |
Revision as of 13:46, 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?
$\textbf{(A) } \dfrac{75}{12} \qquad\textbf{(B) } 10 \qquad\textbf{(C) } 12 \qquad\textbf{(D) } 10\sqrt2 \qquad\textbf{(E) } 15 $