AMC 8 1989 Problem 23

AMC8 1989 年第 23 题

立体几何★★★☆☆

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?

一位艺术家有 14 个棱长为 1 米的正方体。她将它们立在地上形成如图所示的雕塑。然后她对雕塑的暴露表面进行涂漆。她涂了多少平方米？

A.21
B.24
C.33
D.37
E.42

正确答案 · Correct Answer

解析 · Solution

Solution 1

The top view of this figure forms a

3\text{ m} \times 3\text{ m}

square, so it has area

9\text{ m}^2

The left, right, front, and rear views each consist of six

1\text{ m} \times 1\text{ m}

squares stacked in a pyramid shape, so each of these views has an area of

6\text{ m}^2

. So, these views have a total area of

4 \cdot 6 = 24 \text{ m}^2

Therefore, the total painted area is

9 + 24 = 33 \text{ m}^2

. Note that the bottom is not painted.

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