AMC8 1993

AMC8 1993 · Q17

AMC8 1993 · Q17. It mainly tests Area & perimeter.

Square corners, 5 units on a side, are removed from a 20 unit by 30 unit rectangular sheet of cardboard. The sides are then folded to form an open box. The surface area, in square units, of the interior of the box is

从一张20单位×30单位的矩形硬纸板上切掉四个边长为5单位的正方形角，然后将边折起形成一个开口盒子。盒子内部表面积是（平方单位）

(A) 300 300

(B) 500 500

(D) 600 600

(E) 1000 1000

Answer

Correct choice: (B)

正确答案：（B）

Solution

The interior (or exterior) has the same surface area as one side of the sheet of cardboard after the corners have been removed. The area of the sheet is $30\times20=600$ and the area of each square corner removed is $5\times5=25$, so the answer is $600-(4\times25)=500$.

盒子的内表面（或外表面）面积等于剪去四个角后纸板一面的面积。纸板面积为 $30\times20=600$，每个剪去的正方形角面积为 $5\times5=25$，所以面积为 $600-4\times25=500$。

Topics

GE.007 Area & perimeter