Terry 用纸板制作了一个正方体。随后，Terry 制作了 9 个相同的纸板正方体，组成了如下图所示的几何体 P。（图中指示了俯视图、主视图和侧视图。）

(a)
在下方网格中再画出 2 个正方形，以完成 Terry 制作的正方体的展开图。
(b)
在下方点阵网格上画出几何体 P 的主视图。
(c)
将所有正方体重新排列并粘在一起组成几何体 Q，使得当整个几何体 Q（包括底面）被涂成蓝色时，未被涂色面的数量尽可能少。一共有多少个面被涂成了蓝色？

四边形分类 English

先不看答案，让 AI 诊断你卡在哪里？

它不会直接告诉你答案，而是问你卡在哪一步看看 AI 是怎么陪你一步步弄懂这道题的

完整解法

13(b)

1. Determine the maximum height of each column when viewed from the front.

Looking from the front, the solid is divided into 3 columns (left, centre, right).

The left column has a maximum height of 2 cubes (due to the stack at the left-back position).
The centre column has a maximum height of 1 cube.
The right column has a maximum height of 1 cube.

答案

A 2D shape made of 4 squares: a bottom row of 3 squares, and 1 square on top of the left-most square.

13(c)

1. Determine the condition for the least possible unpainted faces

To minimise the number of unpainted faces, we must maximise the number of painted faces. The painted faces are the exposed faces of the solid. Thus, we need to arrange the 9 cubes to form a solid with the maximum possible surface area.

2. Find the maximum number of exposed faces for 9 cubes

Each of the 9 cubes has 6 faces, giving a total of $9 \times 6 = 54$ faces.
When cubes are glued together, each glued connection hides 2 faces (one from each cube).
To maximise the exposed faces, we must minimise the number of glued connections.
The minimum number of connections to keep 9 cubes together as a single solid is 8 (forming a straight line or a simple tree structure without loops).
Number of hidden faces = $8 \times 2 = 16$ .
Number of exposed (painted) faces = $54 - 16 = 38$ .

答案

$34$

AI 分析，可能出错

用 AI 批改，圈出写错的那一步，并自动将你的薄弱点存入错题本，形成你的错因库。

Terry 用纸板制作了一个正方体。 随后，Terry 制作了 9 个相同的纸板正方体，组成了如下图所示的几何体 P。（图中指示了俯视图、主视图和侧视图。）

完整解法

13(b)

13(c)

同一知识点的其他题

Terry 用纸板制作了一个正方体。随后，Terry 制作了 9 个相同的纸板正方体，组成了如下图所示的几何体 P。（图中指示了俯视图、主视图和侧视图。）