Question

一个长方体的六个面都是长方形，尺寸为 $1$ 英尺乘 $3$ 英尺乘 $9$ 英尺。从长方体顶部切掉一个边长为一英尺的立方体，形成一个凹口；这个凹口贯穿整个一英尺的深度（从前面到后面），并位于九英尺长的方向上。新立体的表面积与原立体相比，多了或少了多少平方英尺？

All six faces of a rectangular solid are rectangles, and the solid measures $1$ foot by $3$ feet by $9$ feet. A one-foot cube is cut out of the top of the solid to form a notch; the notch spans the full one-foot depth (from the front face to the back face) and lies partway along the nine-foot length. The total number of square feet in the surface of the new solid is how many more or less than that of the original solid?

少 $2$

$2$ less

少 $1$

$1$ less

相同

the same

多 $1$

$1$ more

多 $2$

$2$ more

答案：C

知识点：表面积立体几何

难度评级：1140

解答：

被切掉的小立方体有三个面原来在立体表面上：上面、前面、后面，所以移除了 $3$ 平方英尺表面积。

切出凹口后，又露出三个新面：凹口底面和两个侧壁，共增加 $3$ 平方英尺。因此表面积不变。

所以正确答案是 C。

The removed cube had three faces on the surface of the solid (top, front, and back), so $3$ square feet of surface are removed.

Cutting it out exposes three new faces (the floor of the notch and its two side walls), adding $3$ square feet. The surface area is unchanged.

Thus, the correct answer is C .

1991 AMC 8 第 15 题

答案：C

难度评级：1140

解答：

其他年份的第 15 题