Problem

1997 AHSME Problem 23

[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 A, E, and F are isosceles right triangles; B, C, and D are squares with sides of length 1; and G 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

\textbf{(A)}\ 1/2\qquad\textbf{(B)}\ 2/3\qquad\textbf{(C)}\ 3/4\qquad\textbf{(D)}\ 5/6\qquad\textbf{(E)}\ 4/3

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.


Show/Hide Problem Tags

Problem Tags: No tags
Want to contribute problems and receive full credit? Click here to add your problem!
Please report any issues to us in our Discord server
Go to previous contest problem (SHIFT + Left Arrow) Go to next contest problem (SHIFT + Right Arrow)
Category: AHSME
Points: 3
Back to practice
Train more like this