Question

一位艺术家把 $14$ 个边长为 $1$ 米的正方体堆成阶梯形：地面上是一个 $3 \times 3$ 的方块层，共 $9$ 个正方体；上面在一个后角对齐放一个 $2 \times 2$ 的方块层，共 $4$ 个正方体；最上面同一角再放一个正方体。她给所有露出的表面上漆，但不漆放在地面上的面。需要上漆的面积是多少平方米？

An artist stacks $14$ cubes, each with edges of $1$ meter, into a staircase: a $3 \times 3$ block of $9$ cubes rests on the ground, a $2 \times 2$ block of $4$ cubes sits on top of it flush into one back corner, and a single cube sits on top of that at the same corner. She paints the entire exposed surface of the sculpture, meaning every face except those resting on the ground. How many square meters does she paint?

$21$

$24$

$33$

$37$

$42$

答案：C

知识点：表面积正方体

难度评级：1050

解答：

从每个竖直方向看，露出的阶梯侧面积是 $3 + 2 + 1 = 6$ 。四个方向共 $4 \times 6 = 24$ 平方米。

从上方看，露出的顶面覆盖整个 $3 \times 3$ 的底面投影，所以顶面积是 $9$ 平方米。底面不漆，因此总上漆面积是 $24 + 9 = 33$ 平方米。

所以正确答案是 C。

Because each higher layer is flush into one corner, each of the four vertical sides shows a stepped profile of $3 + 2 + 1 = 6$ exposed square faces, for $4 \times 6 = 24$ side faces.

Viewed from directly above, the top faces cover the full $3 \times 3$ footprint, adding $9$ more faces. The bottom rests on the ground and is not painted, so the total is $24 + 9 = 33$ square meters.

Thus, the correct answer is C .

1989 AMC 8 第 23 题

答案：C

难度评级：1050

解答：

其他年份的第 23 题