Difference between revisions of "1997 AHSME Problems/Problem 23"
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| + | ==Problem== | ||
| + | |||
| + | <asy> | ||
| + | defaultpen(linewidth(.8pt)+fontsize(10pt)); | ||
| + | draw((-1,1)--(2,1)); | ||
| + | draw((-1,0)--(1,0)); | ||
| + | draw((-1,1)--(-1,0)); | ||
| + | draw((0,-1)--(0,3)); | ||
| + | draw((1,2)--(1,0)); | ||
| + | draw((-1,1)--(1,1)); | ||
| + | draw((0,2)--(1,2)); | ||
| + | draw((0,3)--(1,2)); | ||
| + | draw((0,-1)--(2,1)); | ||
| + | draw((0,-1)--((0,-1) + sqrt(2)*dir(-15))); | ||
| + | draw(((0,-1) + sqrt(2)*dir(-15))--(1,0)); | ||
| + | label("$\textbf{A}$",foot((0,2),(0,3),(1,2)),SW); | ||
| + | label("$\textbf{B}$",midpoint((0,1)--(1,2))); | ||
| + | label("$\textbf{C}$",midpoint((-1,0)--(0,1))); | ||
| + | label("$\textbf{D}$",midpoint((0,0)--(1,1))); | ||
| + | label("$\textbf{E}$",midpoint((1,0)--(2,1)),NW); | ||
| + | label("$\textbf{F}$",midpoint((0,-1)--(1,0)),NW); | ||
| + | label("$\textbf{G}$",midpoint((0,-1)--(1,0)),2SE);</asy> | ||
| + | |||
| + | In the figure, polygons <math>A</math>, <math>E</math>, and <math>F</math> are isosceles right triangles; <math>B</math>, <math>C</math>, and <math>D</math> are squares with sides of length <math>1</math>; and <math>G</math> is an equilateral triangle. The figure can be folded along its edges to form a polyhedron having the polygons as faces. The volume of this polyhedron is | ||
| + | |||
| + | <math> \textbf{(A)}\ 1/2\qquad\textbf{(B)}\ 2/3\qquad\textbf{(C)}\ 3/4\qquad\textbf{(D)}\ 5/6\qquad\textbf{(E)}\ 4/3 </math> | ||
| + | |||
| + | |||
== See also == | == See also == | ||
{{AHSME box|year=1997|num-b=22|num-a=24}} | {{AHSME box|year=1997|num-b=22|num-a=24}} | ||
Revision as of 18:20, 9 August 2011
Problem
![[asy] defaultpen(linewidth(.8pt)+fontsize(10pt)); draw((-1,1)--(2,1)); draw((-1,0)--(1,0)); draw((-1,1)--(-1,0)); draw((0,-1)--(0,3)); draw((1,2)--(1,0)); draw((-1,1)--(1,1)); draw((0,2)--(1,2)); draw((0,3)--(1,2)); draw((0,-1)--(2,1)); draw((0,-1)--((0,-1) + sqrt(2)*dir(-15))); draw(((0,-1) + sqrt(2)*dir(-15))--(1,0)); label("$\textbf{A}$",foot((0,2),(0,3),(1,2)),SW); label("$\textbf{B}$",midpoint((0,1)--(1,2))); label("$\textbf{C}$",midpoint((-1,0)--(0,1))); label("$\textbf{D}$",midpoint((0,0)--(1,1))); label("$\textbf{E}$",midpoint((1,0)--(2,1)),NW); label("$\textbf{F}$",midpoint((0,-1)--(1,0)),NW); label("$\textbf{G}$",midpoint((0,-1)--(1,0)),2SE);[/asy]](http://latex.artofproblemsolving.com/9/1/3/91325d9632e007df3668fcd3ca515a69c0e17548.png)
In the figure, polygons 
, 
, and 
are isosceles right triangles; 
, 
, and 
are squares with sides of length 
; and 
is an equilateral triangle. The figure can be folded along its edges to form a polyhedron having the polygons as faces. The volume of this polyhedron is
See also
| 1997 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 22 |
Followed by Problem 24 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
