Question

一位艺术家有 $14$ 个边长为 $1$ 米的正方体。她把它们放在地面上，搭成如图所示的雕塑，然后给雕塑露出的表面上漆。她一共要漆多少平方米？

An artist has $14$ cubes, each with an edge of $1$ meter. She stands them on the ground to form a sculpture as shown. She then paints the exposed surface of the sculpture. 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

小提示：

分别数四个竖直侧面的露出面积，再加上从上方看到的面积

Count the exposed faces on the four vertical sides, then the faces seen from directly above

大提示：

每个侧面看到的阶梯面积是 $6$ ，上表面的投影覆盖整个 $3 \times 3$ 底面

Each of the four sides shows $6$ exposed faces, and looking straight down covers the full $3 \times 3$ footprint of top faces

解答：

因为每一层都靠齐在同一个角上，所以从每个竖直方向看，露出的阶梯侧面都是 $3 + 2 + 1 = 6$ 个小正方形面，四个方向共 $4 \times 6 = 24$ 个侧面。

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

小提示：

大提示：

解答：

其他年份的第 23 题