Question

图中实线围成的多边形由 $4$ 个全等正方形边对边连接而成。现在在标出的九个位置之一，沿一条边再接上一个全等正方形。所得九个多边形中，有多少个可以折成一个缺少一个面的立方体？

The polygon enclosed by the solid lines in the figure consists of $4$ congruent squares joined edge-to-edge. One more congruent square is attached to an edge at one of the nine positions indicated. How many of the nine resulting polygons can be folded to form a cube with one face missing?

$2$

$3$

$4$

$5$

$6$

答案：E

知识点：展开图（立体几何）正方体

难度评级：1410

解答：

先折起四个阴影正方形。它们占据立方体的四个不同面，留下两个空面。

逐一检查标号位置：位置 $1,$ $2,$ 和 $3$ 会使新正方形折到已被阴影正方形占据的面上。位置 $4,$ $5,$ $6,$ $7,$ $8,$ 和 $9$ 会使它折到两个空面之一。因此 $9$ 个多边形中恰有 $6$ 个可行。

所以正确答案是 E。

Fold the four shaded squares first. They occupy four distinct faces of the cube, leaving two faces open.

Checking the numbered attachments, positions $1,$ $2,$ and $3$ fold the new square onto a face already occupied by one of the shaded squares. Positions $4,$ $5,$ $6,$ $7,$ $8,$ and $9$ fold it onto one of the two open faces. Therefore exactly $6$ of the $9$ polygons work.

Thus, the correct answer is E.

2003 AMC 10A 第 10 题

答案：E

难度评级：1410

解答：

其他年份的第 10 题